1. Introduction to Functions
31 January 2011

2. Functions – What do we remember about them?
Think-Pair-Share
Think about functions for 30 s. independently and silently
Talk about functions for 1 m in your groups
Share as a class

3. Review: Definition
Function – a set (of points, an equation, or a graph) where each input has exactly one output

4. Review: Function Notation
Domain (Input)
Range (Output)
Equation x y
y = x2 – 4
f(x)
f(x) = x2 – 4
In function notation, f(x) replaces y.

5. Review: Function Notation
f(x) = x2 – 4
Pronounced f of x = x2 – 4
The variable inside the parentheses indicates which variable the function is in terms of (the variable used in the function)
f( ) identifies the equation as a function
You may also see other letters, ex. g( ) or h( )

6. Evaluating Functions f(#) f(x) = #
Find the value of f(x) when x equals #.
Solve for f(x)!
f(x) = #
Find the value of x when f(x) equals #.
Solve for x!

7. Find f(#) f(x) = 2x – 10; f(6) f(x) = 2x – 10 f(6) = 2(6) – 10
The value of x is 6. Replace x with 6 in the function and solve for f(6).

8. Find f(#) – Showing Work
f(x) = 2x – 10; f(6)
f(x) = 2x – 10
f(6) = 2(6) – 10
f(6) = 12 – 10
f(6) = 2

9. Example
g(x) = –x2 + 4x + 1
g(2)
g(½)

10. Your Turn:
Complete the 1st 2 columns of problems 1 – 4 on the “Evaluating Functions” handout

11. Answers: f(1) = –1; f(–3) = –9 h(2) = 0; h(1.5) = –0.75
g(0) = ; g(3) = undefined
f(2) = 1; f(–2) = –1

12. Find f(#) When the # Is an Expression
You can also evaluate functions with expressions
f(x) = 2x – 10; f(x+1)
f(x) = 2x – 10
f(x+1) = 2(x+1) – 10
f(x+1) = 2x + 2 – 10
f(x+1) = 2x – 8

13. Find f(#) When the # Is an Expression – Showing Work
f(x) = 2x – 10; f(x+1)
f(x) = 2x – 10
f(x+1) = 2(x+1) – 10
f(x+1) = 2x + 2 – 10
f(x+1) = 2x – 8

14. Example
g(x) = –x2 + 4x + 1
g(x3)
g(x + 2)

15. Your Turn:
Complete the 3rd (and last) column of problems 1 – 4 on the “Evaluating Functions and Domain” handout

16. Find f(x) = #
Remember, we’re solving for values of x that equal that indicated number.
f(x) = 2x – 10; find f(x) = 0
f(x) = 2x – 10
0 = 2x – 10
10 = 2x
5 = x

17. Find f(x) = # – Showing Work
f(x) = 2x – 10; find f(x) = 0
f(x) = 2x – 10
0 = 2x – 10
10 = 2x
5 = x

18. Example 1
f(x) = 2x2 – 3x + 1
Find f(x) = 3

19. Example 2
Find g(x) = 8

20. Your Turn:
Complete problems 5 – 8 on the “Evaluating Functions” handout