Name: ____________________________________
Review for Quiz
Date: ____________
CC Algebra II
Directions: All of your work and solutions (excepts for graphs) should be shown on a separate sheet of paper.
1. Solve for the variable (Round to the nearest 10th where necessary):
1
  2
 16 
(a) log x 
(b) log x 1 27   3
(e) 3ln(a) – ln(5) = ln(25)
(f)
(h) log7(x) =
1
log7(16) + 2log7(3)
4

(c) log2(m) = 5
1
log( x  2)  2
2
(d) log N = 3.8609
(g) log9(x) + log9(x – 8) = 1
(i) logb(16) – logb(x) = logb(x) – logb(4)
(j) 4ln(3x) = 8
2. In the accompanying diagram, figure b is the reflection of y = 2 x in the line y = x.
What is the equation of b?

3. Given the function f(x) = {(6,8), (2,-4), (10,-2), (4,4)}. Find f -1(x).
4. Algebraically, find the inverse of each of the following functions:
1
x-5
3
(a) f(x) = (x + 2)3
(b) g(x) =
(c) h(x) = 3x – 4
(d) p(x) = log2(x) + 1
(e) q(x) = ln(x – 6)
5. a) Sketch the graph of the functions f ( x)  3 x and g ( x)  log 3 x .
b) Considering the graphs, describe the relationship between f(x) and g(x).
c) Specify the domain and range of f and g.
y
x
x
6. (a) For what value of k with the graph of y = 10 contain the point (k, 1)?
(b) For what value of k will the graph of y = log10(x) contain the point (1, k)?

7. Sketch the inverse of each of the following functions:
(a)
(b)
x
1
8. Sketch the graph of the function f(x) =   on the accompanying set of axes and answer the questions that follow.
2
y
(a) What are the domain and range of f(x)?
(b) Identify the end behavior of f(x).
(c) What is the equation of the asymptote of f(x)?
(d) Identify the y-intercept of f(x).
(e) For each of the following transformations on f(x),
would the domain, range, asymptote, and/or y-intercept be changed?
If so, how?
1
i. g(x) = 2  
2
x
x
1
ii. h(x)=   + 2
2
1
iii. p(x) =  
2
x
x 1
9. Use the properties of exponents to show why the graphs of f(x) = 4x and g(x) = 22x are identical.
Hint: Re-write f(x) with a base of 2.
1 𝑥−3
10. Given the function 𝑔(𝑥) = ( )
, write the function g(x) as an exponential function with base 4.
4
Describe the transformations that would take the graph of f(x) = 4x to the graph of g(x).
11. Describe the function below as a transformation of the graph of an
exponential function in the general form ( f(x) = 2x). Sketch the graph of
f(x) and the graph of g(x) by hand. Label key features such as intercepts,
increasing or decreasing intervals, and the horizontal asymptote.
y
g(x) = 22x + 3
x
12. The function graphed below can be expressed as a transformation of the graph of f(x) = log(x).
Write an algebraic function for the transformed graph and state the domain and range.
13. Graph each pair of functions by first graphing f(x) and then graphing g(x) by applying transformations of the graph of
f(x). Describe the graph of g(x) as a transformation of the graph of f(x).
 1 
x
 100 
b) f(x) = log(x) and g(x) = log 
a) f(x) = log3(x) and g(x) = 2log3(x – 1)
Hint: The log of a product is equal to the sum of the logs
y
y
x
x
Answers
1. (a) x = 4
(b) x = 2
(c) m = 32
(d)N = 7259.4
(e) a = 5
(f) 9998
(g) 9
(h) 18
(i) x = 8
9. Show an appropriate justification for:
f(x) = g(x) = 22x
10. g(x) = 4-x + 3
Translation 2 units left,
THEN reflection over the x-axis.
11. Graph
Horizontal scaling by 1/2, then translation up 3 units
e2
(j) x 
3
f(x)  y-int: (0,1),
increasing:  ,   ,
asymptote: y =0
2. y = log2(x)
3. f -1(x) = {(8,6), (-4,2), (-2,10), (4, 4)}
4. (a) f 1 ( x)  3 x  2
(b) g-1(x) = 3x + 15
(c) h-1(x) = log3(x) + 4
(d) p-1(x) = 2x-1
(e) q-1(x) = ex + 6
12. Graph
g(x) = log(x) + 2
Domain: 0,   , Range:  ,  
5. (a) Graph
(b) Inverse Functions
(c) f  Domain:  ,   , Range: 0,  
g  Domain: 0,   , Range:  ,  
(b) k = 0
7. (a) Graph
(b) Graph
8. (a) Domain:  ,   , Range: 0,  
x  
x
f (x)  
f ( x)  0
(c) y = 0
(d) (0,1)
(e) i. y-intercept: (0,2)
ii. y-intercept: (0,3)
Range: 2,  
asymptote: y = 2


13 (a) Graph
Vertical stretch scale factor 2,
then horizontal translation 1 unit to the right.
(b) Graph
Vertical translation down 2 units.
6. (a) k = 0
(b)
g(x)  y-int: (0,4),
increasing:  ,   ,
asymptote: y = 3
1
2
iii. y-intercept:  0, 