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,1.1 Four Ways to Represent a Function
1. The graphs of f(x) and g(x) are given. For what values of x is f(x) = g(x)?
a. 2, 3
b. 0
c. –1
d. –2, 5
e. –2, 10
ANSWER: e
POINTS: 1
DIFFICULTY: Medium
REFERENCES: SCalcET7 1.1.4b SCalc7e 1.1.4b
QUESTION TYPE: Multi-Mode (Multiple choice)
HAS VARIABLES: True
STUDENT ENTRY MODE: Basic
LEARNING OBJECTIVES: PCALC.COH.LO.01.01.12 - Express a function numerically, given its verbal,
algebraic,or graphical representation.
OTHER: Bimodal
NOTES: SCalcET7 Section 1.1 SCalc7e Section 1.1
DATE CREATED: 7/20/2015 1:44 PM
DATE MODIFIED: 2/24/2020 9:14 AM
2. Which of the following functions is neither even nor odd?
a.
b.
c.
ANSWER: b
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,1.1 Four Ways to Represent a Function
POINTS: 1
DIFFICULTY: Medium
REFERENCES: SCalcET7 1.1.78 SCalc7e 1.1.78
QUESTION TYPE: Multi-Mode (Multiple choice)
HAS VARIABLES: True
STUDENT ENTRY MODE: Basic
LEARNING OBJECTIVES: PCALC.COH.LO.01.04.03 - Determine if a function is odd or even algebraically.
OTHER: Bimodal
NOTES: SCalcET7 Section 1.1 SCalc7e Section 1.1
DATE CREATED: 7/20/2015 1:44 PM
DATE MODIFIED: 1/18/2021 10:52 AM
3. If the point is on the graph of an even function, what other point must also be on the graph?
a.
b.
c. (0, 0)
d.
e. None of these
ANSWER: d
POINTS: 1
DIFFICULTY: Medium
REFERENCES: SCalcET7 1.1.71a SCalc7e 1.1.71a
QUESTION TYPE: Multi-Mode (Multiple choice)
HAS VARIABLES: True
STUDENT ENTRY MODE: Basic
LEARNING OBJECTIVES: PCALC.COH.LO.01.04.05 - Describe the symmetry present in the graph of an
even function.
OTHER: Bimodal
NOTES: SCalcET7 Section 1.1 SCalc7e Section 1.1
DATE CREATED: 7/20/2015 1:44 PM
DATE MODIFIED: 1/29/2020 2:43 AM
4. If , evaluate the difference quotient .
a. 2a + h – 8
b. 2a – 8
c. 2a – h – 8
d. h
e. none of these
ANSWER: e
POINTS: 1
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,1.1 Four Ways to Represent a Function
DIFFICULTY: Medium
REFERENCES: SCalcET7 1.1.28 SCalc7e 1.1.28
QUESTION TYPE: Multi-Mode (Multiple choice)
HAS VARIABLES: True
STUDENT ENTRY MODE: Basic
LEARNING OBJECTIVES: PCALC.COH.LO.01.01.08 - Evaluate functions for given values of the independent
variable.
OTHER: Bimodal
NOTES: SCalcET7 Section 1.1 SCalc7e Section 1.1
DATE CREATED: 7/20/2015 1:44 PM
DATE MODIFIED: 1/29/2020 2:48 AM
5. A box with an open top is to be constructed from a rectangular piece of card board with dimensions b = 6 in.
by a = 25 in. by cutting out equal squares of side x at each corner and then folding up the sides as in the figure.
Express the volume V of the box as a function of x.
a.
b.
c.
d.
e.
ANSWER: e
POINTS: 1
DIFFICULTY: Medium
REFERENCES: SCalcET7 1.1.63 SCalc7e 1.1.63
QUESTION TYPE: Multi-Mode (Multiple choice)
HAS VARIABLES: True
STUDENT ENTRY MODE: Basic
LEARNING OBJECTIVES: PCALC.COH.LO.01.01.11 - Express a function algebraically, given its verbal or
numerical representation.
OTHER: Bimodal
NOTES: SCalcET7 Section 1.1 SCalc7e Section 1.1
DATE CREATED: 7/20/2015 1:44 PM
DATE MODIFIED: 2/10/2020 1:32 AM
6. Find an expression for the function y = f(x) whose graph is the bottom half of the parabola
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,1.1 Four Ways to Represent a Function
.
a.
b.
c.
d.
e.
ANSWER: a
POINTS: 1
DIFFICULTY: Medium
REFERENCES: SCalcET7 1.1.53 SCalc7e 1.1.53
QUESTION TYPE: Multi-Mode (Multiple choice)
HAS VARIABLES: True
STUDENT ENTRY MODE: Basic
LEARNING OBJECTIVES: PCALC.COH.LO.01.01.11 - Express a function algebraically, given its verbal or
numerical representation.
OTHER: Bimodal
NOTES: SCalcET7 Section 1.1 SCalc7e Section 1.1
DATE CREATED: 7/20/2015 1:44 PM
DATE MODIFIED: 1/29/2020 3:39 AM
7. A rectangle has perimeter 14 m. Express the area of the rectangle as a function A(l) of the length l of one of
its sides.
a.
b.
c.
d.
e.
ANSWER: a
POINTS: 1
DIFFICULTY: Medium
REFERENCES: SCalcET7 1.1.57 SCalc7e 1.1.57
QUESTION TYPE: Multi-Mode (Multiple choice)
HAS VARIABLES: True
STUDENT ENTRY MODE: Basic
LEARNING OBJECTIVES: PCALC.COH.LO.01.01.11 - Express a function algebraically, given its verbal or
numerical representation.
OTHER: Bimodal
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,1.1 Four Ways to Represent a Function
NOTES: SCalcET7 Section 1.1 SCalc7e Section 1.1
DATE CREATED: 7/20/2015 1:44 PM
DATE MODIFIED: 1/29/2020 3:44 AM
8. If , find and simplify , where h ≠ 0.
a.
b.
c.
d.
ANSWER: d
POINTS: 1
DIFFICULTY: Easy
REFERENCES: SCalcET7 1.1.27 SCalc7e 1.1.27
QUESTION TYPE: Multi-Mode (Multiple choice)
HAS VARIABLES: True
STUDENT ENTRY MODE: Basic
LEARNING OBJECTIVES: PCALC.COH.LO.01.01.08 - Evaluate functions for given values of the independent
variable.
OTHER: Bimodal
NOTES: SCalcET7 Section 1.1 SCalc7e Section 1.1
DATE CREATED: 7/20/2015 1:44 PM
DATE MODIFIED: 1/29/2020 3:59 AM
9. Find the domain and sketch the graph of the function. What is its range?
a. D: (–∞, ∞); R: [–2, ∞) b. D: (–∞, ∞); R: (–∞, 0]
c. D: (–∞, ∞); R: [0, ∞) d. D: (–∞, ∞); R: (–∞, ∞)
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,1.1 Four Ways to Represent a Function
ANSWER: d
POINTS: 1
DIFFICULTY: Medium
REFERENCES: SCalcET7 1.1.49 SCalc7e 1.1.49
QUESTION TYPE: Multi-Mode (Multiple choice)
HAS VARIABLES: True
STUDENT ENTRY MODE: Basic
LEARNING OBJECTIVES: PCALC.COH.LO.01.01.03 - Define range of a function.
OTHER: Bimodal
NOTES: SCalcET7 Section 1.1 SCalc7e Section 1.1
DATE CREATED: 7/20/2015 1:44 PM
DATE MODIFIED: 2/25/2020 12:34 AM
10. Determine whether the function whose graph is given is even, odd, or neither.
a. Even
b. Neither
c. Odd
ANSWER: c
POINTS: 1
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,1.1 Four Ways to Represent a Function
DIFFICULTY: Medium
REFERENCES: SCalcET7 1.1.69 SCalc7e 1.1.69
QUESTION TYPE: Multi-Mode (Multiple choice)
HAS VARIABLES: True
STUDENT ENTRY MODE: Basic
LEARNING OBJECTIVES: PCALC.COH.LO.01.04.04 - Determine if a function is odd or even graphically.
OTHER: Bimodal
NOTES: SCalcET7 Section 1.1 SCalc7e Section 1.1
DATE CREATED: 7/20/2015 1:44 PM
DATE MODIFIED: 2/3/2020 8:06 AM
11. Sandy wishes to have a rectangular garden in her backyard. She has 50 ft of fencing with which to enclose
her garden. Letting x denote the width of the garden, find a function f in the variable x that gives the area of the
garden.
a. f(x) = 50x – x2, 0 < x < 25
b. f(x) = 25x – x2, 0 < x < 25
c. f(x) = 50x – x2, 0 < x < 50
d. f(x) = 25x – x2, 0 < x < 50
ANSWER: b
POINTS: 1
DIFFICULTY: Medium
REFERENCES: SCalcET7 1.1.62 SCalc7e 1.1.62
QUESTION TYPE: Multi-Mode (Multiple choice)
HAS VARIABLES: True
STUDENT ENTRY MODE: Basic
LEARNING OBJECTIVES: PCALC.COH.LO.01.01.11 - Express a function algebraically, given its verbal or
numerical representation.
OTHER: Bimodal
NOTES: SCalcET7 Section 1.1 SCalc7e Section 1.1
DATE CREATED: 7/20/2015 1:44 PM
DATE MODIFIED: 2/10/2020 4:17 AM
12. The graph of the function f is given. State the value of f(2.7).
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, 1.1 Four Ways to Represent a Function
a. f(2.7) = –40
b. f(2.7) = –10
c. f(2.7) = 40
d. f(2.7) = 0
e. f(2.7) = 10
ANSWER: c
POINTS: 1
DIFFICULTY: Medium
REFERENCES: SCalcET7 1.1.3b SCalc7e 1.1.3b
QUESTION TYPE: Multi-Mode (Multiple choice)
HAS VARIABLES: True
STUDENT ENTRY MODE: Basic
LEARNING OBJECTIVES: PCALC.COH.LO.01.02.03 - Identify the value of a function from its graph.
KEYWORDS: 7ET
OTHER: Bimodal
NOTES: SCalcET7 Section 1.1 SCalc7e Section 1.1
DATE CREATED: 7/20/2015 1:44 PM
DATE MODIFIED: 2/25/2020 12:37 AM
13. The graph shown gives the weight of a certain person as a function of age. Find the age at which the person
stopped an exercise program.
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