AnswersCommon Core Algebra I - MA3109 A-ICPerformance Task: Construct and Analyze Piecewise Functions

Performance Task: Construct and Analyze Piecewise Functions — Cumulative exam Answers

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A 2-column table with 9 rows. The first column is labeled x with entries negative 8, negative 6, negative 4, negative 2, 0, 2, 4, 6. The second column is labeled f of x with entries negative 16, negative 8, 0, 8, 16, 32, 64, 128.

Question illustration
(
(–8, –2)
(
(–8, 0)
(
(–∞, –6)
(
(–∞, –4)
2
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Which best describes the relationship between the successive terms in the sequence shown?9, –1, –11, –21, …

A
The common difference is –10.
B
The common difference is 10.
C
The common ratio is –9.
D
The common ratio is 9.
3

Consider the function represented by the equation x – y = 3. What is the equation written in function notation, with x as the independent variable?

f
f(x) = y + 3
f
f(x) = –y – 3
f
f(x) = –x + 3
f
f(x) = x – 3
4

Which equation can be used to represent "six added to twice the sum of a number and four is equal to one-half of the difference of three and the number”?

A
6 + 2(x + 4) = (3 – x)
Option A
B
6 + 2(x + 4) = (x – 3)
Option B
C
(6 + 2)(x + 4) = (3 – x)
Option C
D
(6 + 2)(x + 4) = (x – 3)
Option D
5

Which graph represents a function?

A
Option
B
Option
C
Option
D
Option
6

Karl rides his bicycle 120 feet in 10 seconds. How many feet does he ride in 1 minute?

A
2 feet
B
12 feet
C
720 feet
D
7,200 feet
7

Which description of the graph of the linear inequality y > 3x – 8 is correct?

A
The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded below the line.
B
The graph will be a solid line with a y-intercept of three and a slope of negative eight. The graph will be shaded above the line.
C
The graph will be a solid line with a y-intercept of three and a slope of negative eight. The graph will be shaded below the line.
D
The graph will be a dashed line with a y-intercept of negative eight and a slope of three. The graph will be shaded above the line.
8

two

T
The function g(x) is defined for all real numbers x.
T
The maximum value of the range is 4.
T
The maximum value of the domain is 3.
T
The range of g(x) is {y| –1 < y ≤ 4}.
T
The domain of g(x) is {x| –4 < x ≤ 3}.
9

A sequence is defined by the recursive function f(n + 1) = f(n) – 2.

A
1
B
6
C
8
D
30
10

Martin has a combination of 33 quarters and dimes worth a total of $6. Which system of linear equations can be used to find the number of quarters, q, and the number of dimes, d, Martin has?

A
q + d = 6 25q + 10d = 33
B
q + d = 6 0.25q + 0.1d = 33
C
q + d = 33 25q + 10d = 6
D
q + d = 33 0.25q + 0.1d = 6
11

Which table represents a linear function?

A
Option
Option A
B
Option
Option B
C
Option
Option C
D
Option
Option D
12

Which ordered pairs are in the solution set of the system of linear inequalities?y > x + 2y < 2x + 3

Question illustration
A
(2, 2), (3, 1), (4, 2)
B
(2, 2), (3, –1), (4, 1)
C
(2, 2), (1, –2), (0, 2)
D
(2, 2), (1, 2), (2, 0)
13

Consider the equation v + 4 + v = 8. What is the resulting equation after the first step in the solution?

Question illustration
A
v +4 = 8 – v
Option A
B
v +4 = 8
Option B
C
4 + v = 8 – v
Option C
D
2v + 4 = 8
14

The function f(x) is shown on the graph.

Question illustration
A
0 only
B
–6 only
C
–2, 1, or 3 only
D
–6, –2, 1, or 3 only
15

The graph represents a mechanic’s labor costs for a given number of hours of car repair.

Question illustration
A
All repairs requiring 1 hour or less have the same labor cost.
L
Labor costs the same no matter how many hours are used for a repair.
L
Labor costs for a repair are less expensive as the number of hours increases.
T
There is no cost of labor for a repair requiring less than 1 hour.
16

If f(x) = , what is f(7.6)?

Question illustration
A
3
B
3.5
C
3.8
D
4
17

Timmy writes the equation f(x) = x – 1. He then doubles both of the terms on the right side to create the equation g(x) = x – 2. How does the graph of g(x) compare to the graph of f(x)?

Question illustration
A
The line of g(x) is steeper and has a higher y-intercept.
B
The line of g(x) is less steep and has a lower y-intercept.
C
The line of g(x) is steeper and has a lower y-intercept.
D
The line of g(x) is less steep and has a higher y-intercept.
18

Ori needed at least $1.47 in postage to mail an envelope to his cousin overseas. If x represents the number of $0.44 cent stamps he has and y represents the number of $0.10 cent stamps he has, the inequality representing the number of stamps he can use to mail the envelope is 0.44x+0.10y≥1.47.

A
1
B
2
C
3
D
5
19

Mr. Shaw graphs the function f(x) = –5x + 2 for his class. The line contains the point (-2, 12). What is the point-slope form of the equation of the line he graphed?

y
y – 12 = –5(x + 2)
y
y – 12 = 2(x + 2)
y
y + 12 = 2(x – 2)
y
y + 12 = –5(x – 2)
20

On a coordinate plane, a curved line with minimum values of (negative 0.44, negative 4.3) and (3, negative 4), and a maximum value of (1.7, 0.7), crosses the x-axis at (negative 2.5, 0), (1.3, 0), (2, 0), and (3.44, 0), and crosses the y-axis at (0, negative 4).

Question illustration
[
[–4, –2.5]
[
[–2, –1]
[
[1, 2]
[
[2.5, 4]

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