Function Tables and Graphs

Function

• A function is when each input (x-value) corresponds to exactly one output (y- value)

• In other words, when you substitute (x) into an equation there is only one possible answer (y)

Let me show you what I mean• Let’s use the function y = 2x + 5

y = 2(0) + 5 if x = 0 y = 5

x y

0 5

2

5

10

20

Fill in the function table for the function y = 4x – 3

x y

0

2

5

10

20

Fill in the function table for the function y = 4x – 3

x y

0 -3

2 5

5 17

10 37

20 77

Fill in the function table for the function y = -3x + 5

x y

0

2

5

-2

-5

Fill in the function table for the function y = -3x + 5

x y

0 5

2 -1

5 -10

-2 11

-5 20

This should be an Olympic sport!

Fill in the function table for the function y = x - 4

x y

0

2

5

-2

-5

Fill in the function table for the function y = x - 4

x y

0 -4

2 -3

5 -1

-2 -5

-5 -6

Graphing a Function from a Function Table

• When given a function you can graph it by creating a function table and plotting the points you generate.

• You can pick any points for x and substitute them into the function for the output y

• You should plot at least 5 points to get a good idea of what your graph looks like: 0, two positive numbers, and two negative numbers.

Let’s Use the Functions We Worked With Earlier

y = 2x + 5

x y

0

2

5

-2

-5

Let’s Use the Functions We Worked With Earlier

y = 2x + 5

x y

0 5

2 9

5 15

-2 1

-5 -5

y = 4x – 3

x y

0

2

5

-2

-5

y = 4x – 3

x y

0 -3

2 5

5 17

-2 -11

-5 -23

Two of our points go way off our graph.It helps to show how steep the slope is.

y = -3x + 5

x y

0

2

5

-2

-5

y = x - 4

x y

0

2

5

-2

-5

Closure

• With a partner, graph the function y = -3x + 3

y = -3x + 3

x y