5.3

Function Rules, Tables, & Graphs

List some pairs of numbers that will satisfy the equation x + y = 4.

x = 1 and y = 3x = 2 and y = 2x = 4 and y = 0

What about negative numbers?If x = -1 then y = ?

y = 5

x + y = 4What about decimals?

If x = 2.6 then y = ?

y = 1.4Now, let’s graph the pairs of numbers

we have listed.

(1, 3) (2, 2) (4, 0) (-1, 5) (2.6, 1.4)

Connect the points on your graph.What does the graph look like?

• ••

•

•

It is a straight line! It is a linear relation.

All solutions for theequation x+y=4!

Is (3, -1) a solution to this equation?NO! You can check by graphing it or

plugging into the equation!

• ••

•

•What does the line

represent?

5.3 – Function Rules, Graphs, Tables

A function can be written as:1) Rule:

f(x) = 2x + 3

5.3 – Function Rules, Graphs, Tables

A function can be written as:2) Table

X Y=2x +3 (x,y)

1 2(1)+3=5 (1, 5)

2 2(2)+3=7 (2, 7)

3 2(3)+3=9 (3, 9)

5.3 – Function Rules, Graphs, Tables

A function can be written as:3) Graph

               

               

               

               

               

               

               

               

5.3 – Function Rules, Graphs, Tables

• Continuous Data – Data where the numbers between any two points have value. Connect the points with a smooth (straight) line. Examples: length, weight and distance.

               

               

               

               

               

               

               

               

5.3 – Function Rules, Graphs, Tables

• Discrete Data – Data that involves counting whole numbers. Don’t connect the points. Examples: cars, people and dogs.

               

               

               

               

               

               

               

               

5.3 – Function Rules, Graphs, Tables

• Graphing functions – be careful when you connect the points in a function. Some require a straight line, some a curved line.

y = |x| + 1 y = x + 1               

               

               

               

               

               

               

               

               

               

               

               

               

               

               

               

Let’s review tables!Graph y = 2x + 1 using the domain {0, 1, 4}

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32

1. Make sure the equation is solved for y.

2. Create a t-table using the domain values.

3. Plug in the domain values and solve for the range.

4. Plot the points and connect them to create the line.

x y=2x+1 y

0

1

4

Let’s review the graphing calculator!Graph y = 2x + 1

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21 22 23 24 25 26 27 28 29 30 31 32

1. Select TABLE from the Main Menu2. Make sure the equation is solved for y. Type

in the right side of the equation.3. Select TABL (F6) from the options4. Type the domain values and press EXE5. Select G-CON from the options. This plots

the points and connects them to form the line.