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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21
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Emma earns $6 each time she mows the lawn and $8 per hour for babysitting. She is saving up to buy a new pair of jeans that cost $48. If she mows the lawn x times and babysits for y hours, which graph shows the amount of work she needs to complete to earn at least enough to purchase the new jeans?

A
Option
B
Option
C
Option
D
Option
22
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Ray was in charge of filling the soccer team’s water jug for practice. At the beginning of practice he filled the jug. Halfway through practice the team took a water break. After the break Ray refilled the jug so the players could have water after practice. At the end of practice Ray drained the jug. Which graph could represent the level of the water in the jug during and after practice?

A
Option
B
Option
C
Option
D
Option
23

On a coordinate plane, a curved line, labeled f of x, with a minimum value of (negative 1.9, negative 5.7) and a maximum value of (0, 2) crosses the x-axis at (negative 2.5, 0), (negative 0.75, 0), and (0.75, 0), and crosses the y-axis at (0, 2).

Question illustration
A
F(x) < 0 over the intervals (–∞, –2.5) and (–0.75, 0.75).
B
F(x) > 0 over the intervals (–∞, –2.5) and (–0.75, 0.75).
C
F(x) < 0 over the intervals ( –2.5, –0.75) and (–0.75, ∞).
D
F(x) > 0 over the intervals ( –2.5, –0.75) and (0.75, ∞).
24

Manny has 48 feet of wood. He wants to use all of it to create a border around a garden. The equation can be used to find the length and width of the garden, where l is the length and w is the width of the garden. If Manny makes the garden 15 feet long, how wide should the garden be?

Question illustration
A
9 feet
B
18 feet
C
30 feet
D
33 feet
25

The function f(t) represents the cost to connect to the Internet at an online gaming store. It is a function of t, the time in minutes spent on the Internet.f(t) =Which statement is true about the Internet connection cost?

Question illustration
A
It costs $5 per hour to connect to the Internet at the gaming store.
B
The first half hour is free, and then it costs $5 per minute to connect to the Internet.
C
It costs $10 for each 90 minutes spent connected to the Internet at the gaming store.
D
Any amount of time over an hour and a half would cost $10.
26

How many solutions does this linear system have?y = x+ 2 6x – 4y = –10

Question illustration
A
one solution: (–0.6, –1.6)
B
one solution: (–0.6, 1.6)
C
no solution
D
infinite number of solutions
27

On a coordinate plane, a curved line with minimum values of (negative 2, 0) and (2.4, negative 51) and a maximum value of (negative 0.75, 6), crosses the x-axis at (negative 2, 0), (0, 0), and (3.5, 0), and crosses the y-axis at (0, 0).

Question illustration
A
As the x-values go to positive infinity, the function's values go to negative infinity.
B
As the x-values go to zero, the function's values go to positive infinity.
C
As the x-values go to negative infinity, the function's values are equal to zero.
D
As the x-values go to negative infinity, the function's values go to positive infinity.
28

Gerri purchases a coupon book with discounts for her favorite coffee shop. Every coupon for the coffee shop offers the same discount. The table shows her total savings, y, based on the number of coupons, x, used from the book.

Question illustration
A
slope: 2, y-intercept: –20
B
slope: 2, y-intercept: 10
C
slope: 5, y-intercept: –20
D
slope: 5, y-intercept: 10
29

A mapping diagram shows a relation, using arrows, between input and output for the following ordered pairs: (negative 3, negative 4), (0, negative 4), (negative 2, 2), (negative 2, negative 1), (1, negative 3), (3, 7).

Question illustration
A
(–3, –4)
B
(–2, –1)
C
(1, –3)
D
(3, 7)
30

Yesterday, Selma read 75 pages of her book. If she reads at a pace of 2 pages per minute today, which table shows only viable solutions for the total number of pages she has read, y, after x minutes have elapsed?

A
A 2-column table with 4 rows titled Selma's Reading. The first column is labeled minutes of reading (x) with entries 2, 14, 39, 55. The second column is labeled total pages read (y) with entries 79, 101, 153, 185.
Option A
B
A 2-column table with 4 rows titled Selma's Reading. The first column is labeled minutes of reading (x) with entries negative 16, 6, 27, 52. The second column is labeled total pages read (y) with entries 43, 87, 129, 179.
Option B
C
A 2-column table with 4 rows titled Selma's Reading. The first column is labeled minutes of reading (x) with entries 0, 19, 32, 47. The second column is labeled total pages read (y) with entries 0, 113, 139, 169.
Option C
D
A 2-column table with 4 rows titled Selma's Reading. The first column is labeled minutes of reading (x) with entries 0, 11, 20.25, 58. The second column is labeled total pages read (y) with entries 75, 97, 115.5, 191.
Option D
31

Which is the graph of y – 3 = (x + 6)?

Question illustration
A
Option
B
Option
C
Option
D
Option
32

When a number is added to of itself, the result is 24. The equation that models this problem is n + n = 24. What is the value n?

Question illustration
A
n = 18
B
n = 20
C
n = 21
Option C
D
n = 23
Option D
33

What is the missing step in solving the inequality 4(x – 3) + 4 < 10 + 6x?1. The distributive property: 4x – 12 + 4 < 10 + 6x2. Combine like terms: 4x – 8 < 10 + 6x3. The addition property of inequality: 4x < 18 + 6x4. The subtraction property of inequality: –2x < 18 5. The division property of inequality: ________

A
x < –9
B
x > –9
C
x <
Option C
D
x > –
Option D
34

The simple interest formula is I = Prt, where I represents simple interest on an amount, P, for t years at a rate of r, where r is expressed as a decimal.

A
$60
B
$80
C
$90
D
$100
35

This mapping shows a functional relationship.

Question illustration
A
0
B
2
C
3
D
4
36

Shannon graphed the system of equations.7x – 4y= –8y = x – 3What is the closest approximate solution to the system of equations?

Question illustration
A
(–5, –7.2)
B
(–5, –6.8)
C
(–5, –6.2)
D
(–5, –5.9)
37

What is the solution (a, c) to this system of linear equations?2a – 3c = –6 a + 2c = 11

A
(negative StartFraction 76 over 7 EndFraction, StartFraction 17 over 7 EndFraction)
Option A
B
(3, –4)
C
(3, 4)
D
(StartFraction 87 over 7 EndFraction, negative StartFraction 5 over 7 EndFraction)
Option D
38

Gina wants to take dance classes. She compares two dance studios to determine which has the best deal for her. Dance World charges a rate for each class. Toe Tappers charges a rate for each class plus a one-time registration fee. The system of equations shown models the total costs for taking x classes at each.Dance World: y = 15xToe Tappers: y = 25 + 12.5xHow many classes would Gina need to take for the total cost to be the same at both dance studios?

A
10
B
15
C
100
D
150
39

Which is the graph of linear inequality x – 2y ≥ –12?

A
Option
B
Option
C
Option
D
Option
40

Which graph represents the function y = 2x – 4?

A
Option
B
Option
C
Option
D
Option

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