9.5 Functions (work).notebook December 04, 2017

9.5 FunctionsA function is a relation in which each element of the domain is paired with

exactly one element of the range.

Example 1Is {(5,‐2), (3,2), (4,‐1), (‐2,2)} a function? Why or why not?

Example 3Is {(3,2), (8,‐6), (‐6,2), (7,4)} a function? Why or why not?

Example 2Is {(‐1,5), (‐9,4), (‐1,‐4), (3,0)} a function? Why or why not?

9.5 Functions (work).notebook December 04, 2017

Example 4Which mapping represents a function?

3‐549‐1

8‐605

x y

‐74‐28

‐20‐5‐71

yx

Example 5Is the relation represented by the equation x + 2y = 8 a function?

9.5 Functions (work).notebook December 04, 2017

Vertical Line TestIf any vertical line passes through no more than one point of the graph of a relation, then the relation is a function.

Example 6Use the vertical line test to determine if each relation is a function.

Example 7Determine whether the relation is a function.x2 + y = 6

9.5 Functions (work).notebook December 04, 2017

Example 8Determine whether the relation is a function.x2 ‐ y2 = 4

Example 9Determine whether the relation is a function.x = 2

9.5 Functions (work).notebook December 04, 2017

Example 10Determine whether the relation is a function.y = 2

Example 11Determine whether the relation is a function.x3 + 2 = y

9.5 Functions (work).notebook December 04, 2017

Equations that represent functions can be written in function notation. The equation

y = 2x + 1 can be written f(x) = 2x + 1. The symbol f(x) is read "f of x".

**f(x) does NOT represent multiplication!**

If you see f(3), that means you are plugging the value 3 in for x.

Example 12If f(x) = 3x ‐ 7, find each of the following.a) f(2) b) f(‐4) c) 2[f( )]3

4

9.5 Functions (work).notebook December 04, 2017

Example 13If h(x) = ‐x + 8, find each of the following.a) h(‐9) b) h( ) c) 3[h(6)]2

3

Example 14If k(x) = x2 + 4, find each of the following.a) k(‐5) b) k(8) c) ‐4[k( )]1

2

9.5 Functions (work).notebook December 04, 2017

Example 15If j(x) = x2 ‐ 2x + 1, find each of the following.a) j(6a) b) 6[j(a)]

Example 16If g(x) = x3 ‐ 2x ‐ 3, find each of the following.a) g(4a) b) 4[g(a)]