Download Exponential and Logarithmic Functions Review: Graphing, Properties, and Inverses and more Exams Algebra in PDF only on Docsity!
MTH: 160 COLLEGE ALGEBRA NAME_________________________
Chapter 5 Review Please show all your work and place your final answers in the provided spaces.
- Graph the Exponential Functions and complete the characteristics in the boxes below each graph.
- Graph the Logarithmic Functions and complete the characteristics in the boxes below each graph. As x^ ,^ b^ log ax As x^ 0 ,^ b^ log ax
As x^ ,^ b^ log ax Properties of Exponential Functions
,^ 0,^1
x
f x ba a a
Continuous One – to – One
Domain: ,
Range: 0,
Increasing if a 1
Decreasing if 0 a 1
Horizontal Asymptote x^ - Axis
y - intercept: (0, ) b
a 1 0 a 1
As ,^ x bax As ,^ x bax As , x x ba As , x x ba Properties of Logarithmic Functions
f x b log ax , a 0, a 1
Continuous One – to – One
Domain: 0,
Range: ,
Increasing if a 1
Decreasing if 0 a 1
Vertical Asymptote y^ - Axis
x - intercept: ( ,0) b
a 1 0 a 1
As x 0 , b log ax
- Using the 4 steps to finding the inverse of a function, find the inverse of 3 5 ( ) 5 2 Step 1:_________________________ Step 2:_________________________ Step 3:_________________________ Step 4 x f x x
:_________________________
- 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, is given by the exponential function (^) 1800 0.8 t V t 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?
x b 7
- Convert to a logarithmic equation: a) Ans:_______________________ b) e Ans:_______________________
- Convert to an exponential equation: a) Ans:_______________________ b)
log
l
x
y x
23 Ans:_______________________
- Find the logarithm using the change - of - base formula. Give the exact answer and the the approximate answer to the nearest hundredth.
n 86 4.
log 10
3 2
- Solve the exponential equation algebraically. Round your answer to the nearest thousandth. Ans:___________________________
- Solve the logarithmic equation. Ans:___
log log( 30) 3
x
x x
