1. Functions vs Non Functions

2. Recognizing functions
A function has one output value for every input:
f(x) = x2
f(x) = x3
f(x) = 3x
x f(x) 3 6 9 12 15
x f(x)
x f(x) 1 8

3. Recognizing functions
Let’s look at f(x) = √x
x f(x)
√0 = -1
√1 = 1 or -1 -2
√4 = or -2 2
The equation f(x) = √x is NOT a function because for every x value there are 2 possible f(x) values

4. Non Function
f(x) = √x
x f(x) 1 1 1 -1 4 2 4 -2

5. 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
If the vertical line crosses the graph in more than one place, it is not a function

6. Vertical line test
This is NOT a function

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

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