1. 2.1 Relations and Functions

2. In this chapter, you will learn:
What a function is.
Review domain and range.
Linear equations.
Slope.
Slope intercept form y = mx+b.
Point-slope form y – y1 = m(x – x1).
Linear regression.

3. What is a function? FUNCTION FUNCTION
A function is a special type of relation in which each type of domain (x values) is paired of with exactly one range
value (y value).
NOT A FUNCTION
NOT A FUNCTION
FUNCTION
NOT A FUNCTION
FUNCTION

4. Relations and Functions
Suppose we have the relation { (-3,1) , (0,2) , (2,4) } -3 2 1 2 4
FUNCTION
ONE – TO – ONE
DOMAIN
x - values
RANGE
y - values

5. Relations and Functions
Suppose we have the relation { (-1,5) , (1,3) , (4,5) } -1 1 4 5 3
FUNCTION
NOT ONE – TO – ONE

6. Relations and Functions
Suppose we have the relation { (5,6) , (-3,0) , (1,1) , (-3,6) } 5 -3 1 1 6
NOT A FUNCTION

7. Domain Range Domain and Range
The set of all inputs, or x-values of a function.
It is all the x – values that are allowed to be used.
Range
The set of all outputs, or y-values of a function.
It is all the y – values that are represented.

8. Example 1 Domain = ________________ Range = _________________
All x – values or (-∞ , ∞)
Domain = ________________
Range = _________________
Just 4 or {4}

9. Example 2 Domain = ________________ Range = _________________
Just -5 or {-5}
All y – values or (-∞ , ∞)

10. Example 3 Domain = ________________ Range = _________________
All x – values or (-∞ , ∞)
Domain = ________________
Range = _________________
From -6 on up or [-6 , ∞)

11. Example 4 Domain = ________________ Range = _________________
From -6 on up or [-6 , ∞)
Domain = ________________
Range = _________________
All y – values or (-∞ , ∞)

12. Example 5 Domain = ________________ Range = _________________
All x – values or (-∞ , ∞)
Domain = ________________
Range = _________________
All y – values or (-∞ , ∞)

13. Function Notation What is function notation?
Function notation, f(x) , is called “f of x” or “a function of x”.
It is not f times x .
Example: if y = x+2 then we say f(x) = x+2.
If y = 5 when x = 3, then we say f(3) = 5

14. Example 1 f(x) = 3x + 1 3 (5) + 1 = 16 f( 5) = ____________________
3 (13) + 1 = 40
f( 13) = ____________________
3 (-11) + 1 = -32
f( -11) = ____________________

15. Example 2 f(x) = x² + 3x - 5 5² + 3 (5) – 5 = 35
5² + 3 (5) – 5 = 35
f( 5) = ____________________
0² + 3 (0) – 5 = -5
f( 0) = ____________________
4² + 3 (4) – 5 = 23
f( 4) = ____________________