College Algebra
Final Review
Ch 2 (and section 1.2)
1.) Does the relation  1,0 ,  2,3 ,  4,0 represent a function? If it does, state its domain and range.

2.) Find the domain of f  x  

x
.
x 9
2
3.) Find the domain of f  x   2  x .
4.) Determine algebraically whether the function f  x   x3  4 x is even, odd, or neither.
5.) Determine algebraically whether the function f  x  
1 1
  1 is even, odd, or neither.
x4 x2
6.) Sketch a graph of an even function.
Is the graph symmetric with respect to the x-axis, the y-axis, or the origin?
7.) Sketch a graph of an odd function.
Is the graph symmetric with respect to the x-axis, the y-axis, or the origin?
8.) Sketch a graph that does not represent a function.
9.) Sketch a graph that is increasing on the interval  2, 1 , decreasing on the interval  1,1 , and constant on the
interval 1,3 .
10.) Sketch a graph of the function f  x   x  3  2 .
Ch 4
11.) State whether the function f  x   4 x5  3x2  5x  2 is a polynomial function or not. If it is, give its degree. If it is
not, tell why not.
12.) State whether the function f  x   3x 2  5 x
tell why not.
1
2
 2 is a polynomial function or not. If it is, give its degree. If it is not,
College Algebra
Final Review
13.) Find the domain of the rational function R  x  
x2  4
.
x2
Find any vertical, horizontal, or oblique asymptotes.
14.) Find the domain of the rational function R  x  
x2
.
x 2  16
Find any vertical, horizontal, or oblique asymptotes.
15.) Find the remainder R when f  x   8x3  3x2  x  4 is divided by g  x   x  1 . Is g a factor of f ?
16.) Find the remainder R when f  x   x4  x2  2 x  2 is divided by g  x   x  1 . Is g a factor of f ?
17.) Determine the maximum number of zeros the polynomial function f  x   17 x8  3x3  5x 2  5 may have. Then
𝑝
𝑞
list the potential rational zeros ( ) of the polynomial function. Do not find the zeros.
Ch 5
18.) For f  x  
19.) For f  x  
x 1
1
and g  x   , find the domain of  f g  .
x 1
x
x  3 and g  x  
20.) The function f  x  
3
, find the domain of  f g  .
x
2x  3
is one-to-one. Find its inverse.
5x  2
21.) Use the Change-of-Base Formula and a calculator to evaluate log 2 21 .
College Algebra
Final Review
Solve the following equations
22.) log3
x2  2.
23.) 41 2 x  2 .
24.) 5 x  3x 2 .
x
9
25.) Write log 3   as a sum and/or difference of logarithms. Express powers as factors.
3
26.) Write log 2 z as a sum and/or difference of logarithms. Express powers as factors.
27.) Find the amount that results from investing $2000 at 3.5% compounded monthly after a period of three years.
28.) Find the principal needed now to get $250 after 4 years at 7% compounded semi-annually.
y
Ch 10 (and Section 1.5)
29.) Find an equation of a circle in standard form
with center at the point  1, 4  and radius of 3.
x
30.) Find an equation of a circle in standard form
with center at the point  2, 3 and tangent to the x-axis.
y
x
College Algebra
Final Review
31.) Find the standard form of the circle x 2  y 2  2 x  4 y  4  0 .
y
32.) Find the equation of the parabola
with vertex at  2, 3 and focus at  2, 5 .
x
33.) Find the equation of the parabola
with a focus at  3, 4  and directrix the line x  1 .
y
x
34.) Find the equation of the ellipse with center at  0, 0  ,
y
focus at  0, 4  , and vertex at  0,5 .
x
35.) Find the equation of the ellipse with focus at  4,0 
and vertices at  5, 0  .
y
x
36.) Find the center, foci, and vertices of the ellipse
 x  3
4
2
 y  1

9
2
1.
y
x
College Algebra
Final Review
37.) Find the equation of the hyperbola with center at  0, 0  ,
y
focus at  0, 6  , and vertex at  0, 4  .
x
38.) Find the center, vertices, foci, and asymptotes of the hyperbola
x2 y 2

1.
25 9
y
x
39.) Find the center, vertices, foci,
and asymptotes of the hyperbola
y
 y  3
4
2

 x  2
9
2
 1.
x
Identify the equation
40.) 2 x 2  y 2  3x  2 y  0
41.) 2 x 2  3x  2 y  0
42.) 2 x 2  2 y 2  3x  2 y  0
Ch 12

43.) Write out the first five terms of the sequence an    1

n 1
 n  3 

 .
 n  2 
College Algebra
Final Review
Write out the first five terms of the sequence defined recursively by:
44.) a1  3; an 
2
an 1 .
3
45.) a1  3; an  2n  an1 .
3 3 3
2 4 8
46.) The given pattern continues. Write down the nth term of the sequence an  suggested by the pattern 3, , , ,...
47.) The given pattern continues. Write down the nth term of the sequence an  suggested by the pattern
2 3 4
, , ,...
3 4 5
  1 n 1 
48.) Find the common ratio and write out the first four terms of the geometric sequence an   4    .
  2  
49.) Expand  2 x  3 using the Binomial Theorem.
5


4
50.) Expand 3x 2  4 y using the Binomial Theorem.