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MAC 1140 Module 5 Test
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine any local extrema and absolute extrema.
1) g(x) = |x| + 2
A) Local maximum: 2; absolute maximum: 2
C) Local minimum: -2; absolute minimum: -2
B) Local minimum: 0; absolute minimum: 0
D) Local minimum: 2; absolute minimum: 2
Answer: D
Objective: (4.1) Find Extrema from Equation
2) Estimate graphically the local extrema of f(x) = 3x2 + 5x + 4.
A) Local maximum: 1.92; no local minimum
B) No local maximum; local minimum: -0.83
C) Local maximum: 1.92; local minimum: -0.83
D) No local maximum; local minimum: 1.92
Answer: D
Objective: (4.1) Tech: Find Extrema
3) g(x) = -8x2 - 128x - 519
A) Local maximum: -7; absolute maximum: -7
C) Local minimum: -7; absolute minimum: -7
B) No local extrema; absolute maximum: -7
D) Local maximum: 7; absolute maximum: 7
Answer: A
Objective: (4.1) Find Extrema from Equation
4) Use the graph of f to estimate the local extrema.
y
4
3
2
1
-4
-3
-2
-1
1
2
3
4
x
-1
-2
-3
-4
A) Local maximum: approx. 3.66; local minimum: approx. -2.55
B) No local maximum; no local minimum
C) Local maximum: 1; local minimum: 4
D) Local maximum: ∞; local minimum: -∞
Answer: A
Objective: (4.1) Find Extrema of Function from Graph
1
Use the graph of f to determine the intervals where f is increasing and where f is decreasing.
5)
y
5x
A) Decreasing on
B) Decreasing on
C) Decreasing on
D) Decreasing on
x≤
x≤
x≤
x≤
-2, increasing on -2 ≤ x ≤ 1, decreasing on x ≥ 1
-2, increasing on x ≥ -2
-2, increasing on -2 ≤ x ≤ 0, decreasing on 0 ≤ x ≤ 1, increasing on x ≥ 1
0, increasing on x ≥ 0
Answer: C
Objective: (4.1) Find Where Function Increasing/Decreasing from Graph
2
Pick which graph satisfies the given conditions.
6) Polynomial of degree 3 with three distinct real zeros and a positive leading coefficient.
y
x
A)
B)
y
y
x
x
C)
D)
y
y
x
x
Answer: C
Objective: (4.2) Sketch Graph by Hand Given Properties, Degree
Approximate the coordinates of each turning point by graphing f(x) in the standard viewing rectangle. Round to the
nearest hundredth, if necessary.
7) f(x) = -7x2 + 16x - 5
A) (4.14, 1.14)
B) (-1.14, 4.14)
C) (1.14, 4.14)
D) (1.14, -4.14)
Answer: C
Objective: (4.2) Tech: Find Turning Points
3
Graph the function.
8) f(x) = (-3x - 1)(x - 1)2
y
x
A)
B)
y
y
x
x
C)
D)
y
y
x
x
Answer: A
Objective: (4.2) Tech: Graph Polynomial Function
4
The data table has been generated by a linear, quadratic, or cubic function f. All zeros of f are real numbers located in
the interval [-3, 3]. By making a line graph of the data, conjecture the degree of f.
x -3 -2 -1 0 1 2 3
9)
f(x) -7 -5 -3 -1 1 3 5
y
8
6
4
2
-4 -3 -2 -1
-2
1
2
3
4
x
-4
-6
-8
A) 1
B) 2
C) 3
D) 4
Answer: A
Objective: (4.2) Determine Degree of Polynomial from Data
Solve the problem.
10) A(x) = -0.015x3 + 1.05x gives the alcohol level in an average person's blood x hrs after drinking 8 oz of
100-proof whiskey. If the level exceeds 1.5 units, a person is legally drunk. Would a person be drunk after 6
hours?
A) No
B) Yes
Answer: B
Objective: (4.3) Solve Apps: Polynomial Equations
Solve the polynomial equation graphically or numerically. Round to the nearest hundredth if necessary.
11) x3 - 48x - 128 = 0
A) -4, -4, 8
B) -8, -4, 4
C) 4, -4, 8
D) -4, 4, 8
Answer: A
Objective: (4.3) Solve Polynomial Equation Graphically/Numerically
Write the complete factored form of the polynomial f(x), given the indicated zero.
12) f(x) = 12x4 + 63x3 + 96x2 + 45x
- 5 is a zero.
4
A) f(x) = 12x x - 5
4
x-1 x- 3
B) f(x) = 12x x + 5
4
C) f(x) = 12x x - 5
4
x+1 x+ 3
D) f(x) = x x + 5
4
Answer: B
Objective: (4.3) Write Factored Form of Polynomial Given a Zero
5
x+1 x+ 3
x+1 x+ 3
Use the given information about a polynomial function f(x) to write its complete factored form.
13) f(x) = -6x2 + 18x + 108; zeros: 6 and -3
A) f(x) = 6(x - 6)(x + 3)
B) f(x) = -6(x - 6)(x + 3)
C) f(x) = (x - 6)(x + 3)
D) f(x) = -6(x + 6)(x - 3)
Answer: B
Objective: (4.3) Write Factored Form of Polynomial Given Zeros
Divide. Write with positive exponents.
7
2
14) 48x - 42x - 48x
6x
A) 8x6 - 7x - 8
B) 48x6 - 42x - 48
C) 8x7 - 7x2 - 8x
D) 8x7 - 42x2 - 48x
C) 15 - 114i
D) 111 - 30i
C) 50i
D) -50i
Answer: A
Objective: (4.3) Divide Polynomial by Monomial
Multiply and write the result in standard form.
15) (7 - 8i)(9 - 6i)
A) 15 + 114i
B) 48i2 - 114i + 63
Answer: C
Objective: (4.4) Multiply Complex Numbers
Simplify the expression using the imaginary unit i.
16) -2500
A) ±50
B) i
50
Answer: C
Objective: (4.4) Simplify Using the Imaginary Unit
The graph and equation of a polynomial f(x) are given. Determine the number of real zeros and the number of
imaginary zeros.
17) f(x) = x3 + 2x2 - 5x - 6
y
20
15
10
5
-4 -3 -2 -1
-5
1
2
3
4
x
-10
-15
-20
A) Three real zeros; three imaginary zeros
C) One real zero; two imaginary zeros
B) Three real zeros; two imaginary zeros
D) Three real zeros; no imaginary zeros
Answer: D
Objective: (4.4) Predict Number of Zeros Given Graph, Equation
6
Simplify the expression using the imaginary unit i.
18) (-5 + 9i) - 5
A) -10 + 9i
B) 0 - 9i
C) 0 + 9i
D) 10 - 9i
Answer: A
Objective: (4.4) Add/Subtract Complex Numbers
Find the complete factored form of the polynomial f(x) that satisfies the given conditions.
19) Degree 3, leading coefficient -4, zeros at 5, -3i, and 3i
A) f(x) = -4(x + 5)(x2 + 9)
B) f(x) = -4(x - 5)(x - 3i)(x + 3i)
C) f(x) = -4(x - 5)(x2 + 9)
D) f(x) = -4(x + 5)(x - 3i)(x + 3i)
Answer: B
Objective: (4.4) Find Factored Form Given Deg/Zeros/Lead Coefficient
Multiply and write the result in standard form.
20) 3i(-1 - 8i)2
A) -48 - 189i
C) -48i + 48i2 + 192i3
B) -189i
D) -189 + 48i
Answer: A
Objective: (4.4) Multiply Complex Numbers
7