Math 30-1 1

10.2 Product and Quotients of Functions

• Sum• Difference• Product• Quotient

( ) ( ) ( )f g x f x g x

( ) and ( )f x g x are functions that exist and are defined over a domain.

( ) ( ) ( )f g x f x g x

( ) ( ) ( )f g x f x g x

( )( ) , ( ) 0

( )

f f xx g x

g g x

Why are there restrictions on the variable or non-permissible values for a variable?

Math 30-1 2

The product of two linear functions is a

The quotient of two linear functions is a

quadratic function.

rational function.

Determine the product of the functions in simplest form.

2( ) 3f x x ( ) 2g x x

( ) ( )h x fg x( ) ( )f x g x

23 2x x

2( ) 6 9 2h x x x x

3 2( ) 4 3 18h x x x x

Math 30-1 3

Determine the quotient of the functions in simplest form.

( ) 1r x x 4 3 2( ) 2 5 7 5s x x x x x

( ) ( )s

h x xr

( )( )

( )

s xh x

r x

4 3 22 5 7 5( )

1

x x x xh x

x

3 2( ) 3 2 5,h x x x x 1x

Math 30-1 4

Sketch the graph of h(x) = fg(x) Sketch the graph of h(x) = (ff)(x)

Domain

RangeWhat would the graph of h(x) = (f/f)(x) look like?

Math 30-1 5

Sketch the graph of Sketch the graph of ( )g

h x xf

( )

fh x x

g

Domain

Range

| 3x x

| 7y y

Domain

Range

| 2x x 1

|2

y y

Math 30-1 6

Consider the function h(x) to be in the form ( ) ( ) ( )h x f g x k x

Determine the expressions for f(x), g(x), and k(x)

2( ) sin sin cosh

( ) sin sin 1 cosh

( ) sinf

( ) sin 1g

( ) cosk

Math 30-1 7

Assignment

Page 4961, 2, 3, 6, 7, 8, 11, 12, 13C3