TEST 2 REVIEW – MATH 1314
1.
Let f  x   3x  1 and g  x   5x  4 . Give a formula for each:
(a)
 f  g  x 
(b)
 f  g  x 
(c)
 fg  x 
(d)
f 
   x
g
2.
Let f  x   x2  1 and g  x   x  4 . Evaluate each of the following:
(a)
 f  g  2
(b)
 f  g  1
(c)
 fg  6
(d)
 f 
   5
g
(e)
 f  g 3t 
(f)
 fg  6   f  g  1
3.
Let f  x  
(a)
f
4.
Let f  x  
(a)
f
5.
Use the graphs of f and g to evaluate each.
(a)
f
 g 3
(b)
 f / g 2
(c)
f
 g 1
(d)
 fg 4
(e)
 f  g 2
(f)
g  f 2
(g)
 f  g 1
(h)
g  f 3
x  4 and g  x   x 2 . Give a formula for each of the following:
g  x 
(b)
g
f  x 
1
and g  x   x  3 . Give a formula for each of the following:
x
g  x 
(b)
g
f  x 
6.
Tell if the function has an inverse.
7.
Using the graph of the function f, create a table of values for the given points. Then create a
second table of values that can be used to find f
8.
1
, and sketch the graph of f
f x   4 x  9
(b)
f x   7 x  1
(c)
f x   x 3  1
(d)
f x  
(a)
.
Find the inverse of each function.
(a)
9.
1
BONUS: f  x  
1
1 x
2x  3
x 1
Find the vertex of each parabola. Then find the y-intercept and the axis of symmetry for each
parabola. Finally, find a third point on the parabola and graph the parabola.
f x   2x  3  5
2
(b)
f x   2 x 2  x  1
(c)
f x    x 2  2 x  5
10.
Describe the right-hand and left-hand (end) behavior of each graph of the polynomial function.
(a)
f x  
(c)
f x   3x 6  2 x  1
11.
1 3
x  4x
5
(b)
f x   56  2 x  4 x 2  5x 4
(d)
f x   

7 5
x  5x 2  2 x  3
8
For each polynomial, find all the real zeros, the multiplicity of each zero, the end behavior, and
sketch a graph of the function. (These problems are from 3.2)
(a)
f x   x 2  36
(b)
f x   x  3x  2
(c)
f x   x 3  3x 2  4 x  12
(d)
f x   x 3  8x 2  16 x
(e)
f x    x 3  5x 2
(f)
f x   
12.
(a)

2
1
 x  2  2  x  2 2
4
Use long division to find the quotient and the remainder.
x 4  9 x 3  5 x 2  36 x  4
x2  4
(b)
x 4  6 x 3  11x 2  6 x
x 2  3x  2
(b)
3x 3  16 x 2  72
x6
13.
Divide using synthetic division.
(a)
4 x 3  8 x 2  9 x  18
x2
14.
Use synthetic division and the Remainder Theorem to find each function value.
(a)
f x   2 x 3  7 x  3
f 1  ?
(b)
f 0.5  ?
f 2  ?
f 3  ?
f  1  ?
f 5  ?
f  10  ?
f  x   2 x 6  3x 4  x 2  3
f 2  ?
(c)
f  2  ?
f 1  ?
f x   4 x 4  16 x 3  7 x 2  20
f  2  ?
f 1  ?
(c)
x6 1
x 1
15.
Make a list of all possible rational zeros of the function. (You do not have to find the zeros.)
(a)
f x   2 x 4  13x 3  21x 2  2 x  8
(b)
f x   4 x 4  17 x 2  4
(c)
f x   4 x 3  52 x 2  17 x  3
16.
In each problem:
(1) verify the given factors of the function f
(2) find the remaining factor(s) of f
(3) use your results to write the complete factorization of f
(4) list all real zeros of f
Function
Factors
(a)
f x   2 x 3  x 2  5 x  2
( x  2), ( x  1)
(b)
f x   3x 3  2 x 2  19 x  6
( x  3), ( x  2)
(c)
f x   x 4  4 x 3  15x 2  58x  40
( x  5), ( x  4)
(d)
f x   8 x 4  14 x 3  71x 2  10 x  24
( x  2), ( x  4)
17.
Find the rational zeros of each:
(a)
f  x   x 4  x 3  x 2  3x  6
(b)
f  x   2 x 3  3x 2  8 x  3
18.
List the possible rational zeros and use synthetic division to test if the number is a zero. Then
find all other zeros of the function.
(a)
f  x   x 3  3x 2  4 x  2
(b)
f  x   x 3  3x 2  x  5
(c)
f x   x 3  x 2  x  39
(d)
f x   x 3  x  6
19.
Use the given zero to find all the zeros of the function.
Function
Zero
(a)
f x   x 3  x 2  4 x  4
2i
(b)
f x   2 x 3  3x 2  18 x  27
3i