Name:
5th six weeks test review 2015
Date:
Period: 1 2 3 4 5 6 7
Rewrite the following equations into exponential form
1
1) log 3 81 = 4
2) log12 144 = −2
Rewrite the following equations in logarithmic form
3) 4−3 =
1
64
4) 10−3 = 0.001
Write each logarithmic expression as a single log
5) log 2 + log 4 − log 7
6) 2 log 4 + log 2 + log 2
Evaluate the following logarithms.
8) log3 9  log3 36  log3 4
7) log8 128
Solve each equation. Round answers to the nearest hundredth
9) log(3𝑥 − 2) = 3
10) 2 log(2𝑥 + 5) = 4
11) 152𝑥 = 245
12) log 3 (4𝑥 − 12) = log 3 (𝑥 + 15)
Inverse Variations
13) Suppose that x and y vary inversely. Write a function to model an inverse variation when
x = 7 and y = -1.2
14) Given that y varies inversely with the cube of x, when x = -4 and y = -2. What is the value of
x when y = -0.4
For the following equations describe the transformations.
15) f (x)  2 x 4  5
Phase shift: left/right _______
16) y   log2  x  5  3
Phase shift: left/right _______
Vertical Shift: up/down _______
Vertical Shift: up/down _______
Reflection/Stretch/Compression
Reflection/Stretch/Compression
Domain: __________
Domain: __________
Range: ________
Asymptote: _________________
Range: ________
Asymptote: _________________
Graph the following equations, identify the domain, range and asymptotes when stated.
17) y 
18) f ( x)  2 x 2  4
x2 3
Domain: _________
Range: __________
Domain: _________
Range: __________
Asymptote: __________
19) y  log3  x  2   4
20) Given the ordered pairs of (2, 8) and (3, 32), write an
exponential function in form of y  a  b x .
21) What is the equation for the inverse of f ( x)  7 x  3 ?
22) Given the exponential function of y  3x , what is the
equation if the graph is reflected and shifted six units to
the left and four units up?
Domain: _________
Range: __________
Asymptote: __________
23) Given the logarithm y  log4 x , what is the equation if
the graph has been shifted seven units down and three
units to the right?