MTH: 160 COLLEGE ALGEBRA
Chapter 5 Review
NAME_________________________
Please show all your work
and place your final answers in the provided spaces.
1) Graph the Exponential Functions and complete the characteristics in the boxes below each graph.
a 1
Properties of Exponential Functions
0  a 1
f  x   ba x , a  0, a  1
Continuous
One – to – One
Domain:  ,  
Range:  0, 
Increasing if a  1
Decreasing if 0  a  1
Horizontal Asymptote x - Axis
y - intercept: (0, b)
As x  , ba x 
As x  , ba x 
As x  , ba x 
As x  , ba x 
2) Graph the Logarithmic Functions and complete the characteristics in the boxes below each graph.
a 1
Properties of Logarithmic Functions
0  a 1
f  x   b log a x, a  0, a  1
Continuous
One – to – One
Domain:  0, 
Range:  ,  
Increasing if a  1
Decreasing if 0  a  1
Vertical Asymptote y - Axis
As x  , b log a x 
x - intercept: (b,0)

As x  , b log a x 
As x  0 , b log a x 
As x  0 , b log a x 
1
3) Given
f ( x)  3x 2  5
and
f -1( x ) 
x 5
3
a) State the domain and range of f ( x ) and f 1( x ). Write the answer in set builder notation.
Df  ____________________________
Rf  ____________________________
Df 1 =_____________________________
Rf 1  ____________________________
b) Show that f ( x) and f 1 ( x) are inverses.
Given
f ( x)  3x 2  5
and
f -1 ( x ) 
2
x5
3
4) Using the 4 steps to finding the inverse of a function, find the inverse of
f ( x) 
3x  5
5x  2
Step 1:_________________________
Step 2:_________________________
Step 3:_________________________
Step 4:_________________________
5) Salvage Value. A top-quality phone fax copying machine is purchased for $1800. Its value
each year is about 80% of the value of the preceding year. After t years, its value, in dollars,
t
is given by the exponential function V  t   1800  0.8 
a) Sketch the graph of the function.
b) Find the value of the machine after 0 yr, 1yr, 2 yr, 5 yr, and 10 yr.
c) The company decides to replace the machine when its value has declined to $500. After
how long will the machine be replaced?
3
6) Convert to a logarithmic equation:
x
4
3
a)   
9
5
Ans:_______________________
b) e x  69
Ans:_______________________
7) Convert to an exponential equation:
a) log b y 7  x
Ans:_______________________
b) ln 86  4.4543
Ans:_______________________
8) Find the logarithm using the change - of - base formula. Give the exact answer
and the the approximate answer to the nearest hundredth.
log 23 10
4
9) Express in terms of sums and differences of logarithms and simplify your answer.
log a
a 7 b8

a3b 2
Ans:_________________________________
10) Express as a single logarithm and simplify.
1
log x  3log a y  5log a z
2 a
Ans:________________________________
5
11) Solve the exponential equation algebraically. Round your answer to the nearest
thousandth.
53 x 2  18
Ans:___________________________
12) Solve the logarithmic equation.
log x  log( x  30)  3
Ans:___________________________
6