Exam
Name___________________________________
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the inequality. Write the solution set in interval notation.
5h > -1
1)
h -5
2)
-x2 - 12x - 32 ≥ 0
2)
Simplify the expression.
3) log 0.00001
3)
1
512
4)
log8
5)
ln 17
e
1)
4)
5)
Find f(-x) and determine whether f is odd, even, or neither.
6) f (x) = -2x4 - 3x3
6)
List the possible rational zeros.
7) f (x) = 9x4 + 6x3 - 6x + 33
7)
Identify the vertex, axis of symmetry, and intercepts for the graph of the function.
8) g(x) = x2 - 4x - 12
8)
Find two functions f and g such that h(x) = (f ∘ g)(x).
9)
h(x) =
3
5x - 9
9)
Find the indicated function and write its domain in interval notation.
10) m (x) = x + 3, n(x) = x - 1, (m ∘ n)(x) = ?
11)
p(x) = x2 + 6x, q(x) =
2 - x,
q (x) = ?
p
10)
11)
B-1
Identify the location and value of any relative maxima or minima of the function.
12)
12)
y
4
3
2
1
-4 -3 -2 -1
-1
1
2
3
4
x
-2
-3
-4
Find f(x + h) - f(x) for the given function.
h
13)
f (x) = x2 - 6x.
13)
A polynomial f (x) and one of its zeros are given. Find all the zeros.
14) f (x) = x4 - 6x3 + 18x2 + 42x - 175;
3 + 4i is a zero
14)
Determine if the function is odd, even, or neither.
15) f (x) = 4x3 + 5|x5| + 3
15)
Graph the function.
x + 3, for x > 0
t
(
x
)
=
x2, for x ≤ 0
16)
16)
17)
f (x) =
x2
-4x
- 3x - 4
17)
Solve the problem.
18) Use transformations of the graph of y = log x to graph the function.
3
18)
y = log3(x - 7) + 3
19)
Use the graph of y = 3x to graph the function. Write the domain and range in
interval notation.
f (x) = 3x + 5 + 3
Graph the function and write the domain and range in interval notation.
20) f (x) = 2x
B-2
19)
20)
Evaluate the function for the given value of x.
21) f (x) = 2x, g(x) = |x - 2|, (f · g)(1) = ?
22)
21)
f (x) = x2 + 4x, g(x) = 4x - 2, (f ∘ g)(-3) = ?
22)
Graph the function by using a transformation of the graph of y = 1 .
x
23)
f (x) = 1
x-2
23)
A one-to-one function is given. Write an expression for the inverse function.
24) f (x) = x + 7
x+2
Use the remainder theorem to evaluate the polynomial for the given value of x.
25) f (x) = 4x4 - 5x3 + 24x2 - 30x - 315; f (3)
24)
25)
Use interval notation to write the intervals over which f is (a) increasing, (b) decreasing, and (c) constant.
26)
26)
5
y
4
3
2
1
-5 -4 -3 -2 -1
-1
1
2
3
4
5 x
-2
-3
-4
-5
B-3
Determine if the relation defines y as a one-to-one function of x.
27)
27)
y
4
3
2
1
-4 -3 -2 -1
-1
1
2
3
4
x
-2
-3
-4
Use transformations to graph the given function.
28) f(x) = -x + 2
28)
Sketch the function.
29) f (x) = -x4 + 14x2 - 13
29)
Write the domain in interval notation.
30) f (x) = ln(x2 - 5x + 6)
30)
B-4
Answer Key
Testname: 1314PE2HCCS
1)
2)
3)
4)
5)
6)
7)
8)
-∞, 5 ∪ (5, ∞)
6
[-8, -4]
-5
-3
-7
f (-x) = -2x4 + 3x3; f is neither odd nor even.
±1, ± 1 , ± 1 , ±3, ±11, ±33, ± 11 , ± 11
3 9
3
9
Vertex at (2, -16); axis: x = 2; x-intercepts: (-2, 0) and (6, 0); y-intercept: (0, -12)
3
f (x) = x and g(x) = 5x - 9
10) (m ∘ n)(x) = x + 2; domain: [-2, ∞)
q (x) = 2 - x ; (-∞, -6) ∪ (-6, 0) ∪ (0, 2]
11)
p
x2 + 6x
12) At x = -2, the function has a relative maximum of -1.
At x = 1 the function has a relative minimum of -2.
At x = 4 the function has a relative maximum of 0.
13) 2x + h - 6
14) ± 7, 3 ± 4i
15) neither
9)
16)
y
4
3
2
1
-4 -3 -2 -1
-1
1
2
3
4
x
-2
-3
-4
B-5
Answer Key
Testname: 1314PE2HCCS
17)
y
5
-5
5
x
-5
18)
10
y
5
-10
-5
5
10 x
5
10 x
-5
-10
19)
10
y
5
-10
-5
-5
-10
Domain: (-∞, ∞)
Range: (3, ∞)
B-6
Answer Key
Testname: 1314PE2HCCS
20)
y
10
-5
5
x
Domain: (-∞, ∞)
Range: (0, ∞)
21) (f · g)(1) = 2
22) ( f ∘ g)(-3) = 140
23)
y
5
-5
5
x
-5
24) f -1(x)
= 7 - 2x
x-1
0
a. (-∞, -2) ∪ (2, ∞)
b. never decreasing
c. (-2, 2)
27) No
25)
26)
B-7
Answer Key
Testname: 1314PE2HCCS
28)
y
4
3
2
1
-4 -3 -2 -1
-1
1
2
3
4
x
-2
-3
-4
29)
60
50
40
30
20
10
-5
30)
-10
-20
-30
-40
-50
-60
y
5x
(-∞, 2) ∪ (3, ∞)
B-8