Common Core Algebra Unit 11: Function Notation 2/14/17Lesson 2: Evaluating Functions from a GraphObjective: SWBAT identify and evaluate functions using a graphDo Now: Determine if each graph below is a function. Justify your response.

Group Exploration: Analyzing Graphs of Functions using Function NotationLet’s take a closer look at the graphs from the Do Now and complete a – e below.

The function y = f(x) is defined by the accompanying graph.

a) Find f(5)

b) Find f(-3)

c) Find the value of x when f(x) = 4

d) Find the values of x when f(x) = 2

e) Find the values of x when f(x) = 0

f) Find the value of f(x) = -2

Check for Understanding:The graph of is shown below.

a) Which point could be used to find ?

b) What is the value of f(x)=2?

Partner Practice:The function y = g(x) is defined by the accompanying graph.

a) Find g(2)

b) Find g(6)

c) Find g(0)

d) Find the value of x when g(x) = -4

e) For what values of x is g (x) = 0?

Turn and Talk:The figure below shows the graph of the function y = f(x). The function h is defined by h(x) = -3x + 2. Which statements below are true? Select all that apply. Justify your response.

A. f(-2) is greater than h(-2) C. f(1) is less than h(1)

B. f(0) is greater than h(0) D. When x = -1, f(x) = h(x)

Lesson Summary:Graphs are one of the most powerful ways of visualizing a function’s rule because you can quickly read _____________ given ____________.

Problem Set:1. Given the function y = f(x) defined by the graph below, answer the following questions.(a) Find the value of each of the following:

f 4 f -1 )

(b) For what values of x does f x 2? Illustrate on the graph.

2. Using the graph of the function f x) shown below, answer the following questions.

3.

4.

5. Translate the following statements into coordinate points, then plot them!

6.

6.

7. Find an equation of a linear function given h(1) = 6 and h(4) = –3. (NOTE: Same as write the equation of the line given two points!)

8. Swine flu is attacking Porkopolis. The function below determines how many people have swine where t = time in days and S = the number of people in thousands.

8. Find the missing variable, where f(x) = x2−3 and g(x) = 5x

a. f(2) = b. g(x) = 25

c. g(-15) = d. f(x) = 6

e. f(x) = 33 f. g(3) =

g. g(x) = 1 h. f(-7) =

9. Find the missing variable, using the chart:

a. h(x) = 6 b. h(6) =

c. h(9) = d. h(x) = 2

10. Find the missing variable, using the graph of p(x)

a. p(3) = b. p(x) = 2

c. p(x) = 0 d. p(0) =

5. p(1) = 6. p(x) = -3.5

x h(x)8 36 07 62 49 2

Regents Review Mixed Set:1. Bill spent less than $26 on a magazine and some composition books. The magazine cost $4 and each composition book costs $2.50. a) Write an inequality to find the maximum number of composition books that can be purchased. Be sure to define your variable.

b) Solve the inequality. How many composition books can be purchased?

2. Samantha purchased some red candies and green candies in the ratio of 3:4. The red candies cost $0.50 per ounce and the green candies cost $0.25 per ounce. If the total price of the bag of mixed red and green candies cost $10.00, how many ounces of each type of candy did Samantha purchase?

3. Severe flu cases are increasing in a local hospital. The number of reported cases is shown over the span of a week in the table below.

(a) Using your calculator, determine the equation of the trend line for this data set. Round all values to the nearest tenth.

(b) Using the regression equation that you obtained from your calculator, predict the number of flu cases on Day 10.

(c) To the nearest hundredth, state the correlation coefficient. Using this number, describe the correlation between the two variables.

4. The mathematics department sponsors Math Family Fun Night every year. In the first year, there were 35 participants. In the third year, there were 57 participants.

(a) Assuming the number of participants continues to increase at a constant rate, write an equation that can be used to predict the number of participants, y, for any given year, x. Only an algebraic solution will be accepted.

(b) Based on your equation, how many people are expected to participate in the fifth year?

5. Al is an avid cyclist. On a recent ride, Al encountered some road construction which caused his speed to vary as shown in the graph pictured to the right.

What was Al’s average speed for the time interval 0 ≤ t ≤ 5?

Name ____________________________ Exit Slip

Common Core Algebra Unit 11: Function Notation 2/14/17Lesson 2: Evaluating Functions from a GraphObjective: SWBAT identify and evaluate functions using a graph

Name ____________________________ Exit SlipCommon Core Algebra Unit 11: Function Notation 2/14/17Lesson 2: Evaluating Functions from a GraphObjective: SWBAT identify and evaluate functions using a graph