Download Practice Problems for Test 2

MTH 112
Test 2 Practice Problems Name_______________________
Write the standard form of the equation of the circle with
the given center and radius.
1) (0, 2); 11
The graph of a quadratic function is given. Determine the
functionʹs equation.
6)
y
10
8
Find the center and the radius of the circle.
2) (x + 7)2 + (y + 8)2 = 49
6
4
2
Complete the square and write the equation in standard
form. Then give the center and radius of the circle.
3) x2 + 6x + 9 + y 2 + 16y + 64 = 64
-10 -8 -6 -4 -2-2
4 6 8 10
x
2
4 6 8 10
x
-4
-6
-8
Graph the equation.
4) (x - 5)2 + (y - 3)2 = 9
10
2
-10
y
7)
y
10
8
5
-10
-5
5
6
4
10 x
2
-5
-10 -8 -6 -4 -2-2
-4
-6
-10
-8
-10
5) x2 + y 2 + 6x + 4y - 3 = 0
10
y
Use the vertex and intercepts to sketch the graph of the
quadratic function.
8) f(x) = (x - 2)2 - 4
5
y
10
-10
-5
5
10 x
5
-5
-10
-10
-5
5
-5
-10
1
10
x
B)
Determine whether the given quadratic function has a
minimum value or maximum value. Then find the
coordinates of the minimum or maximum point.
9) f(x) = x2 + 2x - 7
10) f(x) = -4x2 + 12x
Classify the polynomial as constant, linear, quadratic,
cubic, or quartic, and determine the leading term, the
leading coefficient, and the degree of the polynomial.
1
11) g(x) = x3 - 10x + 6
3
-10
12) f(x) = 9x2 - 8 + 0.13x - 5x3
C)
Find the correct end behavior diagram for the given
polynomial function.
13) P(x) = 5x3 + 6x2 - 7x + 7
14) P(x) = -x5 - 4x3 - 9x + 5
15) P(x) = 2.56x4 + 1x2 + x - 4
-10
Use the leading-term test to match the function with the
correct graph.
1
16) f(x) = x2 - 6
3
A)
D)
-10
-10
2
D)
17) f(x) = x5 - x3 + x2 + 2
A)
-4
-4
B)
Use substitution to determine whether the given number
is a zero of the given polynomial.
18) 1; P(x) = 9x3 + 8x2 + x - 18
19) 3; P(x) = x4 + 2x2 - 99
Find the zeros of the polynomial function and state the
multiplicity of each.
20) f(x) = (x + 4)2 (x - 1)
-4
21) f(x) = -5x2 (x - 8)(x + 3)3
22) f(x) = (x2 - 16)3
C)
Use the Intermediate Value Theorem to determine
whether the polynomial function has a real zero between
the given integers.
23) f(x) = 2x4 - 5x2 - 6; between 1 and 2
Determine the maximum possible number of turning
points for the graph of the function.
24) f(x) = x2 + 8x3
-4
3
Graph the function.
25) P(x) = -3x(x - 1)(x - 2)
10
Use the Rational Zero Theorem to list all possible rational
zeros for the given function.
32) f(x) = x4 + 3x3 - 5x2 + 5x - 12
y
Find a rational zero of the polynomial function and use it
to find all the zeros of the function.
33) f(x) = x3 + 6x2 - x - 6
5
-10
-5
5
x
34) f(x) = x3 + 3x2 + 4x - 8
-5
Solve the polynomial equation. In order to obtain the first
root, use synthetic division to test the possible rational
roots.
35) x3 - 3x2 - x + 3 = 0
-10
26) f(x) = -(x - 5)3
10
Find the requested polynomial.
36) Find a polynomial function of degree 3 with
-2, 3, 4 as zeros.
y
37) Find a polynomial function of degree 3 with
1
-7 , 0 , as zeros.
2
5
-10
-5
5
x
Find an nth degree polynomial function with real
coefficients satisfying the given conditions.
38) n = 3; 3 and i are zeros; f(2) = 30
-5
39) n = 4; 2i, 5, and -5 are zeros; leading
coefficient is 1
-10
Use synthetic division to find the quotient and the
remainder.
27) (5x 3 + 2x 2 - x) ÷ (x + 2)
Provide the requested response.
40) Suppose that a polynomial function of degree
4 with rational coefficients has 6,
4, 6 as zeros. Find the other zero.
28) (x4 - 5) ÷ (x - 2)
41) Suppose that a polynomial function of degree
4 with rational coefficients has -4, -6, -2 - i as
zeros. Find the other zero.
Use synthetic division to find the function value.
29) f(x) = x3 + 4x2 + 5x + 5; find f(3)
Given that the polynomial function has the given zero,
find the other zeros.
42) f(x) = x3 - 8x2 + 17x - 30; 6
30) f(x) = 5x4 - 3x3 - 3x2 - 8x - 5; find f(2)
Using synthetic division, determine whether the numbers
are zeros of the polynomial.
31) 2, -2; f(x) = x3 - 7x2 - 4x + 28
Find the domain of the rational function.
x + 4
43) f(x) = x2 - 25
4
44) f(x) = (x - 6)(x + 1)
x2 - 9
54) f(x) = 6
x2 - 1
A)
45) g(x) = x - 8
x + 5
y
8
Find the vertical asymptotes, if any, of the graph of the
rational function.
x - 25
46)
2
x - 8x + 15
-8
8
x
8
x
8
x
8
x
-8
7
47) g(x) = x + 5
B)
y
4
48) g(x) = x(x + 7)
8
Find the horizontal asymptote, if any, of the graph of the
rational function.
25x3
49) h(x) = 5x2 + 1
-8
-8
50) f(x) = 4x2 + 2
x2 - 2
C)
y
8
5
51) f(x) = 2
x + 8
-8
Find the slant asymptote, if any, of the graph of the
rational function.
x2 + 7x - 7
52) f(x) = x - 2
-8
D)
6x2
53) f(x) = 9x2 + 5
y
8
Match the equation with the appropriate graph.
-8
-8
5
1
1
Use transformations of f(x) = or f(x) = to graph the
x
x2
Graph the function, showing all asymptotes (those that do
not correspond to an axis) as dashed lines. List the x - and
y-intercepts.
1
57) f(x) = x + 5
rational function.
55) f(x) = 1
+ 2
x - 5
y
10
5
-10
-5
5
10
x
-5
-10
58) f(x) = Sketch the graph of the polynomial function. Use the
rational zeros theorem when finding the zeros.
56) f(x) = 2x3 + x2 - 13x + 6
30
3x + 1
x
y
20
10
-5
5
x
-10
59) f(x) = -20
-30
6
1
x2 + 1
Solve the polynomial inequality and graph the solution
set on a number line. Express the solution set in interval
notation.
60) (x - 2)(x + 5) > 0
Find and simplify the difference quotient
f(x + h) - f(x)
, h≠ 0 for the given function.
h
66) f(x) = x2 + 8x - 5
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Evaluate the piecewise function at the given value of the
independent variable.
67)
5x - 4 if x < -5
f(x) =
-4x - 3 if x ≥ -5
61) x2 - 2x - 24 ≤ 0
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
62) (x + 2)(x - 1)(x - 6) > 0
Determine f(-4).
Identify the intervals where the function is increasing,
decreasing, or constant.
68)
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
Solve the rational inequality and graph the solution set on
a real number line. Express the solution set in interval
notation.
x - 8
63)
< 0
x + 2
5
y
4
3
2
1
-5
-4
-3
-2
-1
1
2
-1
-2
-3
Solve the inequality.
12
10
64)
> x - 5 x + 1
-4
-5
REVIEW FROM TEST 1
Use the graph to determine the functionʹs domain and
range.
65)
6
Solve. Write interval notation.
69) 4x - 8 < -3.2 or 4x - 8 > 3.2
y
5
4
3
2
1
-6 -5 -4 -3 -2 -1
-1
1
2
3
4
5
6 x
-2
-3
-4
-5
-6
7
3
4
5 x
Answer the question. Circle the letter of your choice.
70) How can the graph of f(x) = .3|x - 9| + 1.3 be
obtained from the graph of y = |x|?
A) Shift it horizontally 1.3 units to the right.
Stretch it vertically by a factor of 3. Shift
it 9 units downward.
B) Shift it horizontally 9 units to the left.
Stretch it vertically by a factor of 3. Shift
it 1.3 units upward.
C) Shift it horizontally 3 units to the left.
Shrink it vertically by a factor of .9. Shift
it 1.3 units upward.
D) Shift it horizontally 9 units to the right.
Shrink it vertically by a factor of .3. Shift
it 1.3 units upward.
For the given functions f and g , find the indicated
composition.
71) f(x) = x2 - 2x - 3,
g(x) = x2 + 2x - 4
Find (f∘g)(-3).
Determine which two functions are inverses of each other.
x - 3
x + 3
72) f(x) = g(x) = 2x - 3
h(x) = 2
2
Find the inverse of the one-to-one function.
3
73) f(x) = 8x - 5
8
Answer Key
Testname: TEST 2 PRACTICE PROBS FA10
1) x2 + (y - 2)2 = 121
2) (-7, -8), r = 7
3) (x + 3)2 + (x + 8)2 = 64
(-3, -8), r = 8
4)
y
10
5
-10
-5
10 x
5
-5
-10
Domain = (2, 8), Range = (0, 6)
5)
y
10
5
-10
-5
10 x
5
-5
-10
6) f(x) = (x + 2)2 + 2
7) j(x) = -x2 + 3
8)
y
10
5
-10
-5
5
10
x
-5
-10
9) minimum; - 1, - 8
3
10) maximum; , 9
2
1
1
11) Cubic; x3 ; ; 3
3
3
9
Answer Key
Testname: TEST 2 PRACTICE PROBS FA10
12) Cubic; -5x3 ; -5; 3
13)
14)
15)
16) C
17) B
18) Yes
19) Yes
20) -4, multiplicity 2; 1, multiplicity 1
21) -3, multiplicity 3; 0, multiplicity 2; 8, multiplicity 1
22) 4, multiplicity 3 ; -4, multiplicity 3
23) f(1) = -9 and f(2) = 6; yes
24) 2
25)
10
y
5
-10
-5
5
x
5
x
-5
-10
26)
10
y
5
-10
-5
-5
-10
27) Q(x) = (5x2 - 8x + 15); R(x) = -30
28) Q(x) = x3 + 2x2 + 4x + 8; R(x) = 11
29) 83
30) 23
31) Yes; yes
32) ± 1, ± 2, ± 3, ± 4, ± 6, ± 12
33) {1, -1, -6}
10
Answer Key
Testname: TEST 2 PRACTICE PROBS FA10
34) {1, -2 + 2i, -2 - 2i}
35) {1, -1, 3}
36) f(x) = x3 - 5x2 - 2x + 24
37) f(x) = x3 + 13 2 7
x - x
2
2
38) f(x) = -6x3 + 18x2 - 6x + 18
39) f(x) = x4 - 21x2 - 100
40) - 6
41) -2 + i
42) 1 + 2i, 1 - 2i
43) {x|x ≠ -5, x ≠ 5}
44) (-∞, - 3) ∪ (- 3, 3) ∪ (3, ∞)
45) (-∞, -5) ∪ (-5, ∞)
46) x = 5, x = 3
47) x = -5
48) x = -7, x = 0
49) no horizontal asymptote
50) y = 4
51) y = 0
52) y = x + 9
53) no slant asymptote
54) B
55)
y
10
5
-10
-5
5
10
x
-5
-10
30
y
20
10
-5
5
x
-10
-20
56)
-30
11
Answer Key
Testname: TEST 2 PRACTICE PROBS FA10
57) No x-intercepts, y-intercept: 0, 1
;
5
10
8
6
4
2
-10 -8 -6 -4 -2
-2
-4
-6
2 4 6
8 10
-8
-10
1
58) x-intercept: - , 0 , no y-intercepts ;
3
10
8
6
4
2
-10 -8 -6 -4 -2-2
2 4 6
8 10
-4
-6
-8
-10
59) No x-intercepts, y-intercept: 0, 1 ;
1
0.5
-10 -8 -6 -4 -2
2 4 6
8 10
-0.5
-1
60) (-∞, -5) ∪ (2, ∞)
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
61) [-4, 6]
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
62) (-2, 1) ∪ (6, ∞)
-10-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10
12
Answer Key
Testname: TEST 2 PRACTICE PROBS FA10
63) (-2, 8)
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
64) (-31, -1) or (5, ∞)
65) domain: [0, ∞)
range: [-1, ∞)
66) 2x + h + 8
67) 13
68) (-2, -1) or (3, ∞)
69) (-∞, 1.2) ∪ (2.8, ∞)
70) D
71) 0
72) g(x) and h(x)
5
3
73) f-1 (x) = + 8x 8
13