AnswersPBCSD_Grade_Forgiveness_1200330_Algebra 2_S2_2024Modeling with Exponential and Logarithmic Equations

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How is the graph of transformed to produce the graph of ?

Question illustration
A
The graph is translated left 5 units, compressed vertically by a factor of , and translated up 3 units.
Option A
B
The graph is stretched vertically by a factor of , translated left 5 units, and translated up 3 units.
Option B
C
The graph is translated left 5 units, compressed horizontally by a factor of , and translated down 3 units.
Option C
D
The graph is stretched horizontally by a factor of , translated left 5 units, and translated down 3 units.
Option D
2
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The equation of the piecewise defined function f(x) is below. What is the value of f(1)?

Question illustration
A
f(1) = –2
B
f(1) = –1
C
f(1) = 2
D
f(1) = 3
3

Jamilla solved the inequality and graphed the solution as shown below. What is the value of b and the missing symbol in Jamilla’s inequality?

Question illustration
A
b = –1,
Option A
B
b = –1,
Option B
C
b = 1,
Option C
D
b = 1,
Option D
4

When graphing the function on your graphing calculator, what is the most appropriate viewing window for determining the domain and range of the function?

Question illustration
A
Xmin: –10, Xmax: 10Ymin: –10, Ymax: 10
B
Xmin: –20, Xmax: 20Ymin: –20, Ymax: 20
C
Xmin: –5, Xmax: 5Ymin: –20, Ymax: 20
D
Xmin: –10, Xmax: 10Ymin: –5, Ymax: 5
5

A store uses the expression –2p + 50 to model the number of backpacks it sells per day, where the price, p, can be anywhere from $9 to $15. Which price gives the store the maximum amount of revenue, and what is the maximum revenue? (Revenue = price number of backpacks.)

Question illustration
A
$9.00 per backpack gives the maximum revenue; the maximum revenue is $32.00.
B
$12.00 per backpack gives the maximum revenue; the maximum revenue is $312.00.
C
$12.50 per backpack gives the maximum revenue; the maximum revenue is $312.50.
D
$15.00 per backpack gives the maximum revenue; the maximum revenue is $20.00.
6

The function is used to model the height of an object projected in the air, where h(t) is the height in meters and t is the time in seconds. What are the domain and range of the function h(t)? Round values to the nearest hundredth.

Question illustration
A
domain: [0, 3.85]range: [0, 18.05]
B
domain: range: [1.9,18.05]
Option B
C
domain: [0, 3.85]range: [1.9,18.05]
D
domain: range: [0, 18.05]
Option D
7

A function is graphed on a coordinate grid. As the domain values approach infinity, the range values approach infinity. As the domain values approach negative infinity, the range values approach infinity. To which family of functions might the described function belong?

A
reciprocal
B
square root
C
exponential
D
quadratic
8

What is the domain of the function graphed below?

Question illustration
A
mc023-2.jpg
Option A
B
mc023-3.jpg
Option B
C
mc023-4.jpg
Option C
D
mc023-5.jpg
Option D
9

The standard diameter of a golf ball is 42.67 mm. A golf ball factory does quality control on the balls it manufactures. Golf balls are randomly measured to ensure the correct size. One day, an inspector decides to stop production if the discrepancy in diameter is more than 0.002 mm. Which function could represent this situation?

A
f(x ) = x – |42.67|
B
f(x ) = |x| – 42.67
C
f(x ) = |42.67 – x|
D
f(x ) = 42.67 – |x|
10

If , , and , what is ?

Question illustration
A
mc012-5.jpg
Option A
B
mc012-6.jpg
Option B
C
mc012-7.jpg
Option C
D
mc012-8.jpg
Option D
11

What is the vertex of the absolute value function below?

Question illustration
A
(4, –1)
B
(1, –4)
C
(1, 4)
D
(4, 1)
12

Let and . The graph of is shown below. What is the range of ?

Question illustration
A
y > 0
B
all real numbers except y = 0
C
mc023-6.jpg
Option C
D
all real numbers
13

The graph below represents c, the amount a phone company charges, based on m, the number of minutes the customer uses each month. If there are a maximum of 44,640 minutes in a month, which equation best represents the phone company’s monthly charges?

Question illustration
A
,
Option A
B
,
Option B
C
,
Option C
D
,
Option D
14

Edmundo used a number line to show the solution for the inequality . Which number line shows the solution?

Question illustration
A
mc023-2.jpg
Option A
B
mc023-3.jpg
Option B
C
mc023-4.jpg
Option C
D
mc023-5.jpg
Option D
15

A company manufactures 16-oz boxes of cereal. Boxes are randomly weighted to ensure the correct amount. If the discrepancy in weight is more than 0.15 oz, the production is stopped. What is the range of acceptable values for production to continue?

A
15.15 oz to 16.00 oz
B
15.85 oz to 16.00 oz
C
15.85 oz to 16.15 oz
D
16.15 oz to 16.45 oz
16

Based on the family the graph below belongs to, which equation could represent the graph?

Question illustration
A
y = StartFraction 1 Over x + 2 EndFraction + 3
Option A
B
y = 0.2 Superscript x Baseline + 3
Option B
C
y = x cubed + 3
Option C
D
y = log x + 3
Option D
17

Which of the following accurately shows the range of the function defined below?

Question illustration
A
mc025-2.jpg
Option A
B
mc025-3.jpg
Option B
C
[3, 6]
D
mc025-4.jpg
Option D
18

The graph of is transformed as shown in the graph below. Which equation represents the transformed function?

Question illustration
A
y = x cubed minus 4
Option A
B
y = (x minus 4) cubed
Option B
C
y = (negative x minus 4) cubed
Option C
D
y = (negative x) cubed minus 4
Option D
19

Which piecewise relation defines a function?

A
mc008-1.jpg
Option A
B
mc008-2.jpg
Option B
C
mc008-3.jpg
Option C
D
mc008-4.jpg
Option D
20

What are the domain and range of the function ?

Question illustration
A
domain: range:
Option A
B
domain: range: (0,)
Option B
C
domain: range:
Option C
D
domain: range:
Option D

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