1. Linear, non linear, and non functions
© 2013 Meredith S. Moody
Linear, non linear, and non functions

2. . . . Linear function f(x) = x + 2-1 1 2 3 . .
Linear function – graph is a straight line

3. Non-Linear function f(x) = x2
x f(x) 4 -2 -1 1 1 1 2 4
Non-Linear function – graph is not a straight line

4. Non-Linear function f(x) = x3
x f(x) -8 -2 -1 -1 1 1 2 8
Non-Linear function – graph is not a straight line

5. Non-Linear function f(x) = 𝑥 x f(x) 1 1 or -1 4 2 or -2 9 3 or -3 161
1 or -1 4
2 or -2 9
3 or -3 16
4 or -4

6. Recognizing functions
A function has one output value for every input
f(x) = x+2
f(x) = x2
f(x) = x3
f(x) = 𝑥
x f(x) 3 4 5 6 7
x f(x)
x f(x) 1 8
x f(x) -1 -2
There are x values that go to more than one y value
Each x value goes to one y value
This is NOT a function
These are FUNCTIONS

7. Recognizing functions
A function has one output value for every input
Is the relation a function? x
f(x) 1 2 3 -1 -2
No, there are 2 y values when x = 1

8. Recognizing functions
A function has one output value for every input
Is the relation a function? x
f(x) 1 2 3 -1 -2
Yes, there is only 1 y value for each x value

9. Vertical line test
To decide if a graph shows a function, use a vertical line to see if there are 2 or more y-values for any given x-value For example, the red curve is not a function because it does not pass the vertical line test When x = 1, there are 3 different y values This is NOT a function

10. examples
Identify which graphs show a function No
Yes
Yes No No
Yes

11. try! Which graphs represent functions? Yes Yes No No
© 2013 Meredith S. Moody
Yes No
Yes No