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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1
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The graph represents the data cost for monthly Internet service for a cell phone.

Question illustration
A
C(x) =
Option A
B
C(x) =
Option B
C
C(x) =
Option C
D
C(x) =
Option D
2
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What is the solution to –2(8x – 4) < 2x + 5?

A
x >
Option A
B
x <
Option B
C
x > 6
D
x < 6
3

What is the inverse of the function f(x) = 4x + 8?

A
h(x) = x – 2
Option A
B
h(x) = x + 2
Option B
C
h(x) = x – 2
Option C
D
h(x) = x + 2
Option D
4

A 2-column table with 8 rows. The first column is labeled t with entries negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries negative 54, negative 20, negative 4, 0, negative 2, negative 4, 0, 16.

Question illustration
A
(–4, 1)
B
(–4, –1)
C
(–1,1)
D
(–1, 2)
5

The table shows the total cost of purchasing x same-priced items and a catalog.

Question illustration
A
$4, the cost per item
B
$4, the cost of the catalog
C
$6, the cost per item
D
$6, the cost of the catalog
6

Which graph shows the solution to the system of linear inequalities?2x – 3y <12y < –3

A
Option
B
Option
C
Option
D
Option
7

What is the vertex of the graph of f(x) = |x – 13| + 11?

A
(–11, 13)
B
(–13, 11)
C
(11, 13)
D
(13, 11)
8

Samir, a carpenter, spent $300 on specialty tools to make toy horses for children. For each horse he makes, he spends $75 on supplies. He charges $125 for each horse. How many horses must Samir sell in order to break even?

A
2
B
3
C
4
D
6
9

Which is the graph of linear inequality 6x + 2y > –10?

A
Option
B
Option
C
Option
D
Option
10

A sequence is defined by the recursive function f(n + 1) = f(n). If f(3) = 9 , what is f(1) ?

Question illustration
A
1
B
3
C
27
D
81
11

Which linear function represents the line given by the point-slope equation y – 2 = 4(x – 3)?

A
f(x) = 6x – 1
B
f(x) = 8x – 6
C
f(x) = 4x – 14
D
f(x) = 4x – 10
12

Which system of linear inequalities has the point (2, 1) in its solution set?

A
y less-than negative x + 3. y less-than-or-equal-to one-half x + 3
Option A
B
y less-than negative one-half x + 3. y less-than one-half x.
Option B
C
Option
Option C
D
y less-than one-half x. y less-than-or-equal-to negative one-half x + 2
Option D
13

Which table represents a direct variation function?

A
A table with 6 columns and 2 rows. The first row, x, has the entries, negative 3, negative 1, 2, 5, 10. The second row, y, has the entries, negative 4.5, negative 3.0, negative 1.5, 0.0, 1.5.
Option A
B
A table with 6 columns and 2 rows. The first row, x, has the entries, negative 5.5, negative 4.5, negative 3.5, negative 2.5, negative 1.5. The second row, y, has the entries, 10, 8, 6, 4, 2.
Option B
C
A table with 6 columns and 2 rows. The first row, x, has the entries, negative 5.5, negative 5.5, negative 5.5, negative 5.5, negative 5.5. The second row, y, has the entries, negative 3, negative 1, 2, 5, 10.
Option C
D
A table with 6 columns and 2 rows. The first row, x, has the entries, negative 3, negative 1, 2, 5, 10. The second row, y, has the entries, negative 7.5, negative 2.5, 5.0, 12.5, 25.0.
Option D
14

The tables represent the functions f(x) and g(x).

Question illustration
A
x = –12
B
x = –9
C
x = –6
D
x = –3
15

Which graph represents the function g(x) = |x + 4| + 2?

A
Option
B
Option
C
Option
D
Option
16

The graph represents the function where electricity usage in kilowatts per hour of a clock radio varies directly with the number of days it is plugged into the wall current.

Question illustration
A
0.25 kWh per day
B
0.50 kWh per day
C
2.40 kWh per day
D
4.00 kWh per day
17

Becky created a graph to represent her distance away from home one afternoon. She left home and ran to the park, met some friends and stayed at the park, and then walked back home using the same route. Which graph could Becky have created?

A
Option
B
Option
C
Option
D
Option
18

Marlena created a table of values representing the height in feet, h(t), of a coconut falling to the hard ground with a height of 0 feet, collected over t seconds. Assume the coconut does not bounce and rests on the ground when it lands.

Question illustration
A
The initial height of the coconut is 190 feet.
B
The coconut will hit the ground between 4 and 5 seconds after it was dropped.
C
The values of h(t) when t = 4 and 5 should be 0.
D
The maximum height of the coconut was 1 second after it was dropped.
19

A function g(x) is defined as shown.g(x) = What is the value of g(4)?

Question illustration
A
10
B
12
C
14
D
16
20

Which are points on the graph of y = 1.5 + ⌈x⌉? Select three options (–4.5, –2.5)(–0.8, 0.5)(7.9, 9.5)(4.5, 6)(1.3, 3.5)

A
(–4.5, –2.5)
B
(–0.8, 0.5)
C
(7.9, 9.5)
D
(4.5, 6)
E
(1.3, 3.5)

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