Chapter 5: Functions

Index: A: Introduction to Functions B: Functions – Notation & Evaluating Functions C: Functions – Minimum and Maximum D: Functions – Y-intercepts, X-intercepts, Zeros & Roots E: Functions – Domain & Range F: Functions – Increasing & Decreasing Positive & Negative G: Average Rate of Change H: Piecewise Functions

Name:_____________________________________________________ Date:___________________________ Period:_________ Algebra I Introduction to Functions 1 5A

Relations & Functions A relation is a set of ordered pairs. Example

The domain is the set of all of the x-coordinates from the ordered pairs.

Ex: __________________________

The range is the set of all of the y-coordinates from the ordered pairs.

Ex: __________________________ The graph of a relation is the set of points on a graph equivalent to the ordered pairs in the relation.

Options for representing a relation 1) ____________________________________ 2) ____________________________________ 3) ____________________________________ 4) ____________________________________ 5) ____________________________________ ____________________________________ Ex:

Exercise 1:Using the provided graph, which mapping represents the relation? a) b) c) d) Exercise 2: Express the relation below as a graph.

Relations vs. Functions Relations: A relation is simply a set of ordered pairs. A relation can be any set of ordered pairs and no special rules are applied. Functions: A function is a set of ordered pairs (relation), in which each x – element has ONE y – element associated with it. (no x repeats)

Exercise 3: Identify each of the following as a relation or function.

1) ___________________________ 2) ___________________________ 3) ___________________________

4) ___________________________ 5) ___________________________ 6) ___________________________

Exercise 4: Answer the following questions: _____ 1) Given the relation Which of the following values for x will make relation B a function? (1) 7 (2)9 (3) 4 (4) 5 _____ 2) The following relation is a function. (1) true (2) false _____ 3) Is the relation depicted in the chart below a function?

0 1 3 5 3 9 8 9 10 6 11 7

(1) yes (2) no Vertical Line Test: When examining a graph to determine if it is a relation or function, a vertical line can be drawn through the graph. If the vertical line intersects the graph once, then the graph is a function and if the vertical line intersects the graph more than once, the graph is a relation. Exercise 5: Identify each of the following as a relation or function.

1) ___________________________ 2) ___________________________ 3) ___________________________

Domain Range -4 5 -2 7 0 9 2 11

4) ___________________________ 5) ___________________________

Name:_____________________________________________________ Date:____________________________ Period:_________ Algebra I Introduction to Functions 1 5A HW

_____ 1) Is the relation depicted in the chart below a function?

1 2 3 4 5 6 4 5 6 7 8 9

(1) yes (2) no

_____ 2) Which of the relations is a function?

(1)

(2)

(3)

(4) _____ 3) Which of the relations is not a function?

(1)

(2)

(3)

(4)

_____ 4) In 2013, the United States Postal Service charged $0.46 to mail a letter weighing up to 1 oz. and $0.20 per ounce for each additional ounce. Which function would determine the cost, in dollars, c(z), of mailing a letter weighting z ounces where z in an integer greater than 1? (1) c(z) = 0.46z + 0.20 (2) c(z) = 0.20x + 0.46 (3) c(z) = 0.46(z-1) + 0.20 (4) c(z) = 0.20(z – 1) + 0.46 _____ 5) Which of the ordered pairs is not a function? (1) (2) (3) (4) _____ 6) If the function represents the number of full hours that it takes a person to assemble x sets

of tires in a factory, which would be an appropriate domain for the function? (1) the set of real numbers (2) the set of negative numbers (3) the set of integers (4) the set of non-negative integers

7) Use the vertical line test to determine if it is a function. (a) (b) (c) Review Section: 8) (a) Solve the following inequality: (b) What is the smallest value of x to make this inequality true?

Name:_____________________________________________________ Date:____________________________ Period:_________ Algebra I Introduction to Functions 1 5A HW 1.) (1) 2.) (4) 3.) (3) 4.) (4) 5.) (4) 6.) (4) 7.) a.) Function b.) Relation c.) Relation 8.) a.) b.) The smallest value of x to make the inequality true is .

Homework Answers

Name:_____________________________________________________ Date:___________________________ Period:_________ Algebra I Function Notations & Evaluating 5B The concept of the function ranks near the top of the list in terms of important Algebra concepts. Almost all of higher-level mathematical modeling is based on the concept. Like most important ideas in math, it is relatively simple:

THE DEFINITION OF A FUNCTION A function is a clearly defined rule that converts an input into at most one output.

These rules often come in the form of: (1) equations, (2) graphs, (3) tables, and (4) verbal descriptions.

Function notation can be very, very confusing because it really looks like multiplication due to the parentheses. But, there is no multiplication involved. The notation serves two purposes: (1) to tell us what the rule is and (2) to specify an output for a given input. Since functions are rules that convert inputs (typically x-values) into outputs (typically y-values), it makes sense that they must have their own notation to indicate what the what the rule is, what the input is, and what the output is. In the first exercise, your teacher will explain how to interpret this notation.

Exercise #1: For each of the following functions, find the outputs for the given inputs.

(a) (b)

(c)

Exercise #2: Consider the function rule: multiply the input by two and then subtract one to get the output. (a) Write an equation that gives this rule in symbolic form. (b) What is the output when the input is 8. (c) What input would be needed to produce an output of 17? Exercise #3: A function rule takes an input, n, and converts it into an output, y, by increasing one half of the input by 10. Write an equation rule in symbolic form. Then determine the output for this rule when the input is 50.

Exercise #4: The function is completely defined by the graph shown below. Answer the following questions based on this graph. Find the value of:

Exercise #5: The function is graph on the grid below. Answer the following questions based on this graph. Find the value of:

Name:_____________________________________________________ Date:___________________________ Period:_________ Algebra I Function Notations & Evaluating 5B HW 1.) Given , find the value of 2.) Given , find the value of 3.) Give , find the expression for 4.) Suzie is buying fresh produce from the grocery store. Carrots cost $2.50 per pound. First write a function rule that can represent the total cost of the pounds brought. If Suzie buys three and a half pounds of carrots, what will her total cost be? If Suzies total cost is $21.25 how many pounds of carrots did she buy?

5.) The function is completely defined by the graph shown below. Answer the following questions based on this graph. Find the value of: 6.) Boiling water at 212 degrees Fahrenheit is left in a room that is at 65 degrees Fahrenheit and begins to cool. Temperature readings are taken each hour and are given in the table below. In this scenario, the temperature, T, is a function of the number of hours, h.

(a) Evaluate and (b) For what value of is (c) Between what two consecutive hours will Explain how you arrived at your answer. Review Section: _______ 7.) The product of a number and 3, increased by 5, is 7 less than twice the number. Which equation can be used to find this number, ? [1] [2] [3] [4] _______ 8.) Which value of x is a solution of the inequality ? [1] 13 [2] 14 [3] 15 [4] 16

Name:_____________________________________________________ Date:___________________________ Period:_________ Algebra I Function Notations & Evaluating 5B HW 1.) 2.) 3.) 4.) 8.5 pounds 5.) 6.) a) b) c) will happen between 2 and 3 because 100 falls between 104 and 85. 7.) (1) 8.) (1)

Homework Answers

Name:_____________________________________________________ Date:_________________________ Period:_________ Algebra I Minimum & Maximums 5C

Do Now: Find the value of using the function

.

Exercise #1: Let’s see if there is a quicker and easier way for us to answer the same question. Find the value of

using the function

.

Exercise #2: Using the function find the value of

Exercise #3: Using the function

find the value of

Exercise #4: Using the function

find the value of

Minimum & Maximums Graphs of functions are very complex and contain many different points. Lets look at the provided graph:

The tops of the mountains are relative maximums because they are the highest points in their little neighborhoods (relative to the points right around them).

Suppose you’re in a roomful of people (like the classroom). Find the tallest person there. He is the relative maximum of that room. Specifically, he’s the tallest relative to the people around him. But, what if you took that guy to an NBA convention? There’d be lots of guys who beat him. Look back at the graph… Other than just pointing these things out on the graph, we have a very specific way to write them out. Officially for this graph, we’d say: 1.) F has a maximum of 2 2.) F has a maximum of 1 The maximum is, actually, the height… the x guys is where the maximum occurs. So, saying that the maximum is would be unclear and not really correct. Now for the relative minimums…. Those are the bottoms of the valleys: Relative minimums are the lowest points in their little neighborhoods. 1.) F has a minimum of 2.) F has a minimum of

Now for the absolute maximum and minimums…. These are the highest(maximum) point or lowest (minimum) point over the entire function or relation. Exercise #5: Your turn. Identify the absolute maximum and minimums of the following function.

Exercise #6: State the coordinates of the absolute maximum and the absolute minimum of the following function.

Name:_____________________________________________________ Date:_________________________ Period:_________ Algebra I Minimum & Maximums 5C HW 1.) Given the function defined by the formula find the following algebraically:

(a) (b) (c) (d)

_______ 2.) If the function is defined by

then which of the following is the value of

[1] [2] 2 [3] 14 [4] 7

_______ 3.) If the function and

then which of the following is a true statement?

[1] [2] [3] [4] 4.) Based on the graph of the function shown below, answer the following questions. (a) Evaluate each of the following. Illustrate with a point on the graph. (b) What is the value of the absolute maximum of the function (c) What are the coordinates of the absolute minimum of the function

Review Section: 5.) What is the product of and ? 6.) What is the solution to

Name:_____________________________________________________ Date:_________________________ Period:_________ Algebra I Minimum & Maximums 5C HW

1.)

2.) (1) 3.) (3) 4.) a.) b.) Absolute maximum of 5 c.) Absolute minimum of 5.) 6.)

Homework Answers

Name:_____________________________________________________ Date:_________________________ Period:_________ Algebra I Y-Int, X-Int, Zeros & Roots 5D

The Y- Intercept The y-intercept of a graph is the point at which the function intercepts the y-axis. Each function will only have one y-intercept. Remember that the coordinates of the y-intercept are in the format (0, #).

The y-intercept of the graphed function (parabola) is . Example: The y-intercept of a quadratic equation can be found using the graph. What are the coordinates of the y-intercept of this equation? [1] [2] [3] [4]

The X- Intercept, Zeros & Roots of the function Each of these will represent the same points. The x-intercept(s) of a graph are the point(s) at which the function intercepts the x-axis. Functions can have many different x-intercepts. Each x-intercept will be a coordinate in the format (#, 0).

The x-intercept of the graphed function (parabola) are and . Example: The roots of a quadratic equation can be found using the graph. What are the roots of this equation? [1] only [2] and [3] and 4 [4] and

Exercise #1: Using the graphed function , identify the following. (a) What is the y-intercept? Why is there only one y-intercept? (b) What are the zeros of the function ?

Exercise #2: Using the graph of the function shown below, answer the following questions. (a) Find the value of each of the following: (b) For how many values of x does What are the values for (c) What is the intercept of this relation? (d) State the absolute maximum and absolute minimum values the graph obtains. (e) Explain why the graph above represents a function.

Exercise #3: The function is defined by the graph shown below. It is known as piecewise linear because it is made up of straight line segments. Answer the following questions based on this graph. (a) Evaluate each of the following: (b) For how many values of x does

Name:_____________________________________________________ Date:_________________________ Period:_________ Algebra I Y-Int, X-Int, Zeros & Roots 5D HW 1.) Given the function defined by the formula find the following algebraically: (a) (b) (c) (d) 2.) Physics students drop a ball from the top of a 100 foot high building and model its height above the ground as a function of time with the equation . The height, , is measured in feet and time, , is measured in seconds. Be careful with all calculations in this problem and remember to do the exponent first! (a) Find the value of Include proper units (b) Calculate Does our equation predict that What does this output represent? the ball has hit the ground at 2 seconds? Explain. 3.) If you knew that , then what coordinate point must lie on the graph of ? Explain your reasoning. 4.) The following graph represents the cost of a phone plan after a certain number of text messages used in a month. Analyze the graph to answer the following questions. (a) How much would you have to pay if you used: 500 text messages ________________________ 1800 text messages _________________________ (b) Interpret (c) What might have caused the graph to begin increasing at 800 text messages?

5.) The function is shown graphed over the interval (a) Evaluate each of the following: (b) How many relative maximum values are there for the function . State the values of x where they occur. (c) How many relative minimum values are there for the function . State the values of x where they occur. (d) What are the absolute maximum and minimum values of the function? At what values do they occur? (e) What are the x and intercept(s) of the function? List each of the following as an ordered pair interecept (s): _______________________________ intercept(s): _____________________________________ Review Section: _____ 6.) What is the solution of [1] [2] [3] [4] 7.) Is the following considered a function? Explain why or why not. {(3,4),(-1,3),(3,5),(6,-1)} _____ 8.) When is subtracted from the result is: [1] [2] [3] [4]

Name:_____________________________________________________ Date:_________________________ Period:_________ Algebra I Y-Int, X-Int, Zeros & Roots 5D HW 1.) 2.) a.) At the time zero the height is 100 feet. b.) At 2 seconds the ball doesn’t hit the ground, it is still 36 feet in the air. 3.) 4.) a.) text cost $30 1800 texts cost $80 b.) 1400 text messages will cost $60 c.) The $30 plan only offered 800 text messages per month. 5.) a.) 6.) (1) 7.) Not a function, with appropriate reason 8.) (3)

Homework Answers

Name:_____________________________________________________ Date:_________________________ Period:_________ Algebra I Domain & Range 5E

The Range The range of a function is the complete set of all possible resulting values of the dependent variable (y, usually), after we have substituted the domain. In plain English, the definition means: The range is the resulting y-values we get after substituting all the possible x-values. To find the range of a given function: Lowest Value (Bottom) Highest Value (Top) **Remember: and

will always just be less than! You can also say that the y values are all greater (above) Therefore it can also be written as

Example: The graph given represents the parabolic path of a football thrown by a quarterback during the football game. Identify the range of the graphed parabola.

The Domain In mathematics, the domain of a function is the set of "input" or argument values for which the function is defined. That is, the function provides an "output" or value for each member of the domain.

To find the domain of a given function: Lowest Value (Left) Highest Value (Right) Example: Erin was asked to graph the function Her answer is shown below. Identify the domain of the function from Erin’s graph.

Exercise #1: Using the graphs, identify both the domain and the range using set builder notation. (a) Domain: __________________________________________________ Range: __________________________________________________ (b) Domain: __________________________________________________ Range: __________________________________________________ (c) Domain: __________________________________________________ Range: __________________________________________________

(d) Domain: __________________________________________________ Range: __________________________________________________

Exercise #2: Using the graphs, identify both the domain and the range using interval notation. (e) Domain: __________________________________________________ Range: __________________________________________________ (f) Domain: __________________________________________________ Range: __________________________________________________

(g) Domain: __________________________________________________ Range: __________________________________________________

Name:_____________________________________________________ Date:_________________________ Period:_________ Algebra I Domain & Range 5E HW 1.) Using the graphs, identify both the domain and the range using set builder notation. (a) Domain: __________________________________________________ Range: __________________________________________________ (b) Domain: __________________________________________________ Range: __________________________________________________ (c) Domain: __________________________________________________ Range: __________________________________________________

2.) Using the graphs, identify both the domain and the range using interval notation. (a) Domain: __________________________________________________ Range: __________________________________________________ (b) Domain: __________________________________________________ Range: __________________________________________________ (c) Domain: __________________________________________________ Range: __________________________________________________

3.) The function is shown graphed over the interval (a) Evaluate each of the following: (b) What are the absolute maximum and minimum values? (c) What are the coordinates of the y-intercept? (d) How many zeros does the function have? (e) What is the domain and the range of the function in set builder notation. Review Section: _____ 4.) A model rocket is launched into the air from ground level. The height, in feet, is modeled by , where x is the number of elapsed seconds. What is the total number of seconds the model rocket will be in the air?

[1] 1 [2] 2 [3] 0 [4] 16

5.) Solve algebraically for x: 6.) Carla bought a dress at a sale for 20% off the original price. The sale price of the dress was $28.80. Find the original price of the dress, in dollars.

Name:_____________________________________________________ Date:_________________________ Period:_________ Algebra I Domain & Range 5E HW 1.) a.) b.) c.) 2.) a.) b.) [0, 3] c.) 3.) a.) b.) Absolute maximum is 4 Absolute minimum is c.) d.) 5 zeros e.) Domain: Range: 4.) (2) 5.) 6.) The dress was originally $36.00

Homework Answers

Name:_____________________________________________________ Date:_________________ Period:_________ Algebra I Increasing/Decreasing 5F There is a lot of terminology associated with the graph of a function. Many of the terms have names that are descriptive, but still, work is needed to master the ideas. 1) Increasing is just another way of saying that a graph 2) Decreasing is just another way of saying that a is going up over a given domain “x” interval. We can also graph is going down over a given domain “x” interval. say that its slope is positive. We can also say that its slope is negative.

Lowest Value (Left) Highest Value (Right) Lowest Value (Left) Highest Value (Right) or (4,7) or (7,10) Lowest Value (Left) Highest Value (Right) Lowest Value (Left) Highest Value (Right) or (0, ) or (- ,0)

Let’s look at an example: Check out this graph! You’ve got an ant climbing on the graph. His name is Pierre. Pierre can only crawl from left to right (just like how we read!)

If Pierre is climbing uphill, then the graph is increasing!

So our graph is increasing on two intervals: and ( , -3) (1,4) If Pierre is going downhill, then the graph is decreasing!

So our graph is decreasing on one interval: ( , 1) Think about it…. When Pierre is standing right ON ….he is not going uphill or downhill, he is just standing there! What if Pierre is walking on (4, )? Is it increasing or decreasing?

So now that we have a better understanding about increasing/decreasing, let’s try some examples! Example#1: A ball is thrown into the air from the edge of a 48-foot-high cliff so that it eventually lands on the ground. The graph below shows the height, y, of the ball from the ground after x seconds. For which interval is the ball’s height always decreasing?

[1] [2] [3] [4]

Example#2: Given the function shown below, answer the following questions:

(a) What is the coordinate of the absolute minimum?

(b) What is the coordinate of the y –intercept?

(c) What are the zeroes of the function?

(d) Name an interval that is increasing.

(e) Name an interval that is decreasing.

You can also be asked when a function is positive or negative.

1) Positive: A function is positive when it lies ABOVE 2) Negative: A function is negative when it lies the x-axis. BELOW the x-axis.

Lowest Value (Left) Highest Value (Right) Lowest Value (Left) Highest Value (Right) or (-1,4) or (4,7)

Example#3: The Function is shown graphed below over the interval .

(a) What is the y-intercept of the function? Explain why a function cannot have more than one y-intercept.

(b) Give the x-intercepts of the function. These are also known as the function’s zeroes because they are where

(c) Would you characterize the function as (d) State the interval over which . increasing or decreasing on the domain interval . Explain your answer.

Name:_____________________________________________________ Date:_________________ Period:_________ Algebra I Increasing/Decreasing 5F HW

1) The function y g x is completely defined by the graph shown below. Answer the following questions based

on this graph.

(a) Determine the coordinates of the absolute minimum and maximum represented on this graph.

(b) State the coordinates of the y-intercept. (c) How many roots are there according to this function?

(d) State the domain and range of this function using set builder notation. (e) State an interval over which the function is: Increasing:_______________________________ Decreasing:_____________________________

2) The graph of the function 2 4 1y x x is shown below.

(a) State this function’s y-intercept.

(b) Between what two consecutive integers does the larger x-intercept lie?

(c) State an interval over which the function is: Increasing:_______________________________

Decreasing:_____________________________

y

x

y

x

3) Based on the graph of the function y g x shown below, answer the following questions.

(a) Evaluate 2 , 0 , 3 and 7g g g g .

(b) For what values of x does ?

(c) What values of x solve the equation 0g x

(d) Name an interval that is: Increasing: _________________________________ Decreasing: ________________________________ Positive:____________________________________ Negative: ___________________________________ Review Section:

4) The function 2 5h x x maps the domain given by the set 2, 1, 0,1, 2 . Which of the following sets

represents the range of h x ?

(1) 0, 6,10,12 (3) 5, 6, 9

(2) 5, 6, 7 (4) 1, 4, 5, 6, 9

5) Which of the following represents the range of the quadratic function shown in the graph below?

(1) 4, (3) , 4

(2) , 4 (4) 4,

y

x

y

x

6) One of the following graphs shows a relationship where y is a function of x and one does not.

(a) Draw the vertical line whose equation is 3x on both graphs.

(b) Give all output values for each graph at an input of 3 . Relationship A: Relationship B:

(c) Explain which of these relationships is a function and why. 7) The length of a rectangle is represented by and the width is represented by . (a) Express the perimeter of the rectangle as a trinomial. (b) Express the area of the rectangle as a trinomial. 8) The product of and is: [1] [2] [3] [4]

y

x

Re

lati

on

ship

A

y

x

Re

lati

on

ship

B

Name:_____________________________________________________ Date:_________________ Period:_________ Algebra I Increasing/Decreasing 5F HW 1) (a) Absolute Minimum: (-3,-5) Absolute Maximum: (6,4) (b) (0,2) (c) 3 roots (d) Domain: Range: (e) Increasing: Decreasing: 2) (a) (0,1) (b) between 3 and 4 (c) Increasing: Decreasing: 3) (a) -3, -3, and 0 (b) (c) (d) Increasing: Decreasing: Positive: Negative: 4) (3) 5) (2) 6) (b) -4 and 4; -2 (c) Relationship B with an appropriate reason 7) (a) (b) 8) (3)

Homework Answers

Name:_____________________________________________________ Date:_________________ Period:_________ Algebra I Average Rate of Change 5G Functions are rules that give us outputs when we supply them with inputs. Very often, we want to know how fast the outputs are changing compared to a change in the input values. This is referred to as the average rate of change of a function.

Exercise #1: Finding the average rate of change is the same as finding the _____________ of a line. There is, of course, a formula for finding average rate of change. Let’s get it out of the way.

Exercise #2: Consider the function given by Find its average rate of change from to Carefully show the work that leads to your final answer. Exercise #3: The function is given in the table below. Which of the following gives its average rate of change over the interval ? Show your calculations that lead to your answer.

[1]

[2]

[3]

[4]

Exercise #4: A function is represented by the table provided. What is the average rate of change for the table provided?

Exercise #5: Frances is selling glasses of lemonade. The function

models the number of glasses she

has sold after hours. What is the average rate at which she is selling lemonade between and hours. Include proper units in your answer.

Exercise #6: Find the average rate of change between to .

Name:_____________________________________________________ Date:_________________ Period:_________ Algebra I Average Rate of Change 5G HW 1.) Consider the function given by . Find its average rate of change between the following points. Carefully show the work that leads to your final answer. (a) to (b) to (c) to 2.) The function is given in the table below. Find its average rate of change between the following points. Show the calculations that lead to your answer. (a) to (b) to 3.) The function is given in the graph below. Find its average rate of change between the following points. Show the calculations that lead to your answer. (a) to (b) to

4.) The following table shows the number of points the Arlington girls team scored in their last basketball game where t is the time passed in minutes and the total number of points scored after t minutes. (a) What was the average rate they were shooting in the first half of the game? Be sure to include proper units in your answer. (b) What was their average rate over the whole game? (c) Given your answers above which half of the game do you feel they had a better rate of scoring? Explain. 5.) Consider the function given by (a) Find its average rate of change from to (b) Find its average rate of change from to (c) The average rate of change for this function is always 6 (as you should have found in the first two parts of the problem). What type of function has a constant average rate of change? What do we call this average rate of change in this case? Search the Internet if needed.

Review Section: 6.) What is the product of and ? [1] [2] [3] [4] 7.) If five times a number is less than 55, what is the greatest possible integer value of the number? [1] 12 [2] 11 [3] 10 [4] 9 8.) If n is an odd integer, which equation can be used to find three consecutive odd integers whose sum is [1] [2] [3] [4] 9.) When is subtracted from , the result is: [1] [2] [3] [4]

Name:_____________________________________________________ Date:_________________ Period:_________ Algebra I Average Rate of Change 5G HW 1) (a) (b) (c)

2) (a) (b)

3) (a)

(b)

4) (a) 3 points/minute (b) 2 points/minute (c) First half with reason 5) (a) (b) (c) Linear with reason 6) (3) 7) (3) 8) (3) 9) (4)

Homework Answers

Name:_____________________________________________________ Date:_________________ Period:_________ Algebra I Piecewise Functions 5H Do Now: Given the function , answer the following: (a) Using your calculator, complete the (b) Graph the following on the graph provided. following table.

x y

0

1

2

3

4

Up till now, we have been graphing individual functions like , and Now we are going to graph a function that has more than one piece.

Example: Graph

Each piece must live ONLY in its own neighborhood. Let’s put a fence up so that we don’t make any mistakes.

Now, we just need to figure out who the fence owner is…

So let’s begin by graphing the first part. Since the domain is we will make our table of values less than 1

Now let’s graph the second part. Since the domain is we will make our table of values greater than 1

Exercise #1: Given:

Determine (a) (b) (c)

Exercise #2: Given:

Determine (a) (b) (c)

Exercise #3: Consider the function given by the formula

(a) Evaluate each of the following. (c) Graph on the axes below. (b) Fill out the table below for the inputs given. Keep in mind which formula you are using.

Exercise #4: Consider the function given by the formula

(a) Evaluate each of the following. (c) Graph on the axes below. (b) Fill out the table below for the inputs given. Keep in mind which formula you are using.

x y -3

-2

-1

0

0

1

2

3

x y -3

-2

-1

0

0

1

2

3

4

Name:_____________________________________________________ Date:_________________ Period:_________ Algebra I Piecewise Functions 5H HW

1) Given:

Determine (a) (b) (c)

2) Consider the function defined by:

2 4 4 1

6 1 5

x xf x

x x

(a) Evaluate the following:

(a) (b)

(b) Graph the function f x by graphing each of the two lines.

*We must always include a table of values*

(c) State the range of the function f x .

x y

-4

-3

-2

-1

0

1

1

2

3

4

5

y

x

3) Consider the following relationship given by the formula

(a) Fill out the table and graph on the axes below.

x y

-2

-1

0

1

1

2

Review Section: 4) 5)

Name:_____________________________________________________ Date:_________________ Period:_________ Algebra I Piecewise Functions 5H HW 1) (a) 53 (b) 3 (c) 28 2) (a) 6 and 4 (b) Table and graph (c) 3) (a) Table and graph 4) (2) 5) (4)

Homework Answers