Combining Functions

1
Combining Functions

• Section 1.7

2
Objectives

• Determine the domain and range (where possible)
  of a function given as an equation.
• Add, subtract, multiply, and/or divide function.
• State the domain two function combined in an
  arithmetic method.
• Put together two (or more) functions using
  composition.
• Determine the value of the composition of two (or
  more) functions given the graphs of the
  functions.
• Determine the value of the composition of two (or
  more) function given the equations of the
  functions.
• State the domain two function combined through
  composition.

3
Objectives

• Decompose the composition of two functions into
  it constituent functions.
• Solve a word problem involving the composition of
  functions.

4
Vocabulary

• domain
• range
• function composition

5
Domain Questions

• Does the function have a denominator?
• Does the function have a square or even root?
• Does the function have a log or ln in it?
• Did the function arise from finding an inverse?
• Is this a real world problem?

6
Find the domain of the function
7
Find the domain of the function
8
Find the domain of the function
9
Find the domain of the function
10
Given the functions and
find each of the following
11
Given the functions and
find the domain of each of the following
12
For the functions f(x) and g(x) are given in the
graph below.  Find the indicated corresponding
function values
13
Given the functions and
find each of each of the following
14
Given the functions and
find each of the following
15
Given the functions and
find the domain of each of the following
16
For the functions f(x) and g(x) are given in the
graph below.  Find the indicated corresponding
function values
17
Express the function in the form . If
,find g(x).
18
A spherical weather balloon is being inflated.
The radius of the balloon is increasing at the
rate of 9 cm per second. Express the surface
area of the balloon as a function of time t (in
seconds).