AnswersCR27 ALG 1-1200310-S2-Degele-VOL7006PIntroduction to Modeling with Functions

Introduction to Modeling with Functions — Unit test Answers

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Which graph represents the function f(x) = |x| – 4?

A
On a coordinate plane, an absolute value graph has a vertex at (0, 4).
Option A
B
On a coordinate plane, an absolute value graph has a vertex at (negative 4, 0).
Option B
C
On a coordinate plane, an absolute value graph has a vertex at (0, negative 4).
Option C
D
On a coordinate plane, an absolute value graph has a vertex at (4, 0).
Option D
2
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Daniel is on an airplane flying to a destination 825 miles away. After one hour, the pilot announces that the plane is 495 miles away from its destination airport. In another hour, the pilot announces that the plane will begin its half-hour descent for the final 165 miles.

A
d = 825 – 165t
B
d = 825 – 330t
C
d = 825 + 165t
D
d = 825 + 330t
3

The team mascot shoots a rolled T-shirt from a special T-shirt cannon to a section of people in the stands at a basketball game. The T-shirt starts at a height of 8 feet when it leaves the cannon and 1 second later reaches a maximum height of 24 feet before coming back down to a lucky winner.

A
f(t) = –16(t – 1)2 + 24
B
f(t) = –16(t + 1)2 + 24
C
f(t) = –16(t – 1)2 – 24
D
f(t) = –16(t + 1)2 – 24
4

Which graph represents the function p(x) = |x – 1|?

A
Option
B
Option
C
Option
D
Option
5

Graham uses a 10 by 10 grid to model a decreasing pattern. He cuts off a section representing a percent of the current area so that the remaining area represents the next term in the pattern, rounded to nearest whole centimeter. The area after each cut is shown on the graph.

Question illustration
A
10%
B
20%
C
80%
D
100%
6

If a flowering tree is cared for properly, the number of blossoms produced on the tree will exponentially increase until the tree reaches maturity. Which graph could show y, the number of blossoms expected on a flowering tree, for each year after the young tree is planted, x?

A
A graph shows age of trees (years) labeled 1 to 10 on the horizontal axis and number of blossoms on the vertical axis. A line increases from 0 to 3 years then decreases from 3 to 7 years.
Option A
B
A graph shows age of trees (years) labeled 1 to 10 on the horizontal axis and number of blossoms on the vertical axis. A curved line increases from 0 to 8 years.
Option B
C
A graph shows age of trees (years) labeled 1 to 10 on the horizontal axis and number of blossoms on the vertical axis. A straight line increases from 0 to 9 years.
Option C
D
A graph shows age of trees (years) labeled 1 to 10 on the horizontal axis and number of blossoms on the vertical axis. A curved line decreases from 0 to 9 years.
Option D
7

On a coordinate plane, an absolute value graph has a vertex at (1, 3).

Question illustration
A
g(x) = |x + 1| + 3
B
g(x) = |x + 3| – 1
C
g(x) = |x – 1| + 3
D
g(x) = |x + 3| + 1
8

Which could be the graph of f(x) = |x - h| + k if h and k are both positive?

A
Option
B
Option
C
Option
D
Option
9

Over which interval is the graph of the parent absolute value function decreasing?

Question illustration
A
(–∞, ∞)
B
(–∞, 0)
C
(–6, 0)
D
(0, ∞)
10

On a coordinate plane, an absolute value graph has a vertex at (1, negative 2.5).

Question illustration
A
k = –2.5
B
k = –1
C
k = 1
D
k = 2.5
11

What is the range of the function g(x) = |x – 12| – 2?

A
{y | y > –2}
B
{y | y > –2}
C
{y | y > 12}
D
{y | y > 12}
12

The graph shows the population of a bacteria in an experiment, measured every hour.

Question illustration
A
f(t) = 10(1.4)t
B
f(t) = 10(2.0)t
C
f(t) = 14(1.4)t
D
f(t) = 14(2.0)t
13

Alicia bought a notebook and several erasers at the student store. The graph shows the relationship between the total cost of her items and the number of erasers she purchased.

Question illustration
A
$1.00
B
$1.50
C
$2.00
D
$3.50
14

The graph of f(x) = |x| is translated 6 units to the right and 2 units up to form a new function. Which statement about the range of both functions is true?

A
The range is the same for both functions: {y | y is a real number}.
B
The range is the same for both functions: {y | y > 0}.
C
The range changes from {y | y > 0} to {y | y > 2}.
D
The range changes from {y | y > 0} to {y | y > 6}.
15

The amount of a radioactive substance remaining after t years is given by the function , where m is the initial mass and h is the half-life in years. Iron has a half-life of 2.7 years. Which equation gives the mass of a 200 mg iron sample remaining after t years, and approximately how many milligrams remain after 12 years?

Question illustration
A
; 2.6 mg
Option A
B
f(t)=2.7(0.5)t; 0.0007 mg
C
f(t)=200(0.5)t; 0.05 mg
D
; 9.2 mg
Option D
16

What is the vertex of the graph of g(x) = |x – 8| + 6?

A
(6, 8)
B
(8, 6)
C
(6, –8)
D
(–8, 6)
17

On a coordinate plane, an absolute value graph has a vertex at (negative 2, 1).

Question illustration
A
Both h and k must be positive.
B
Both h and k must be negative.
C
h must be positive and k must be negative.
D
h must be negative and k must be positive.
18

Sophia plots points on a graph to represent the shape of a concave lens.

Question illustration
A
linear
B
exponential
C
quadratic
D
square root
19

On a coordinate plane, an absolute value graph has a vertex at (negative 4, negative 10).

Question illustration
A
g(x) = |x – 4| – 10
B
g(x) = |x + 4| – 10
C
g(x) = |x – 10| + 4
D
g(x) = |x + 10| – 4
20

The graph shows the distance, in feet, required for a car to come to a full stop if the brake is fully applied and the car was initially traveling x miles per hour.

Question illustration
A
y =
Option A
B
y =
Option B
C
y =
Option C
D
y =
Option D

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