Question 1

The cost to manufacture x pairs of sunglasses can be represented by a function, $C(x)$. If it costs $398 to manufacture 4 pairs of sunglasses, which of the following is true?
Select the correct equation.

( *NO CALCULATOR*)

Accepted Answer

$C(4)=398$

Answer

$C(4)=99.50$

Answer

$C(99.50)=1$

Answer

$C(398)=4$

Question 2

A local theater sells admission tickets for $$\$9.00$$ on Thursday nights. At capacity, the theater holds 100 customers. The function $M(n) = 9n$ represents the amount of money the theater takes in on Thursday nights, where $n$ is the number of customers. What is the domain of $M(n)$ in this context?

Accepted Answer

all non-negative integers less than or equal to 100

Answer

all non-negative rational numbers

Answer

all non-negative integers that are multiples of 9

Answer

all whole numbers

Question 3

The function $r(x)$ represents the radius of a circle for a given area, $x$. A graph of the function is shown in the figure.

According to the graph, what is the approximate average rate of change in the radius of the circle as the area increases from 3 square feet to 7 square feet?

Accepted Answer

0.125 foot per square foot

Answer

0.25 foot per square foot

Answer

0.5 foot per square foot

Answer

8 feet per square foot

Question 4

Which graph represents the equation $5y - 3x= -15$?

Accepted Answer

https://uploads.quizalize.com/1b96b803-608b-b879-b14f-3294927d4b31/question/9deb0013-f8e7-9d63-df05-fda955b9eb3f.png

Answer

https://uploads.quizalize.com/1b96b803-608b-b879-b14f-3294927d4b31/question/cd8017b0-7ef8-777c-70ef-d29209b85157.png

Answer

https://uploads.quizalize.com/1b96b803-608b-b879-b14f-3294927d4b31/question/345c15f2-fa7a-5953-efce-2cdc91c7afe8.png

Answer

https://uploads.quizalize.com/1b96b803-608b-b879-b14f-3294927d4b31/question/7676cfef-c861-f209-f240-f85ae7195303.png

Question 5

The area, $A$, in square feet, of a rectangular storage bin in a warehouse is given by the function $A(x)=-2x^2+36x$, where $x$ is the width, in feet, of the storage bin. 
If the function is graphed in a coordinate plane, which statement would be true?

Accepted Answer

The $x$-intercepts of the function are O and 18, which are a lower bound and an upper bound for the possible values of the width of the storage bin.

Answer

The $x$-intercepts of the function are O and 18, which are a lower bound and an upper bound for the possible values of the length of the storage bin.

Answer

The $x$-intercepts of the function are O and 8, which are a lower bound and an upper bound for the possible values of the width of the storage bin.

Answer

The $x$-intercepts of the function are O and 8, which are a lower bound and an upper bound for the possible values of the length of the storage bin.

Question 6

The area, $A$, in square feet, of a rectangular storage bin in a warehouse is given by the function $A(x)=-2x^2+36x$, where $x$ is the width, in feet, of the storage bin. 
The process of completing the square can be used to calculate the width, in feet, of the storage bin that gives a maximum area. What is the missing value? 
$A=-2x^2+36x$
$A=-2(x-9)^2+?$
Enter your answer in the box.

Accepted Answer

162

Question 7

The function $f$ is defined by $f(x) = x ^2 - 2x - 24$. 
If $f(x+3)=x^2+kx-21$, what is the value of $k$?
Enter your answer in the box.

Accepted Answer

4

Question 8

Solve the equation $27^x=9^{x-3}$ for $x$.
Enter your answer in the box.

Accepted Answer

-6

Question 9

The London Eye, a Ferris wheel in England, has a diameter of 120 meters. The wheel completes a full rotation in 30 minutes to allow passengers to enter a capsule at the base of the Ferris wheel without stopping the wheel.  At the highest point, a capsule reaches a height of 135 meters above the ground. The height above the ground, in meters, of a capsule after $x$ minutes can be modeled by $f(x) =A \cdot cos(\frac {\pi}{15}x)+B$, where $A$ and $B$ are constants.

Given the situation, what is the value of $A$?
Enter your answer in the box.

Accepted Answer

-60

Question 10

Consider the polynomial function $f(x) = (2x - 1)(x + 4)(x - 2)$.
What is the $y$-intercept of the graph of the function in the xy-coordinate plane?
Enter your answer in the box.

Accepted Answer

8

Question 11

Consider the polynomial function $f(x) = (2x - 1)(x + 4)(x - 2)$.
What is the end behavior of the graph of the function?

Accepted Answer

As $x \rightarrow - \infty, f(x) \rightarrow - \infty$, and as $x\rightarrow \infty, f(x)\rightarrow \infty$.

Answer

As $x \rightarrow - \infty, f(x) \rightarrow  \infty$, and as $x\rightarrow \infty, f(x)\rightarrow \infty$.

Answer

As $x \rightarrow - \infty, f(x) \rightarrow  \infty$, and as $x\rightarrow \infty, f(x)\rightarrow -\infty$.

Answer

As $x \rightarrow - \infty, f(x) \rightarrow - \infty$, and as $x\rightarrow \infty, f(x)\rightarrow -\infty$.

Question 12

Consider the polynomial function $f(x) = (2x - 1)(x + 4)(x - 2)$.
How many relative maximums does the function have?

Accepted Answer

one

Answer

three

Answer

none

Answer

two

Question 13

The apothem of a regular polygon is the distance from the center to any side.  
If the length of the apothem remains constant at 10 inches, the formula for the perimeter of a regular polygon as a function of the number of sides $n$ is $P(n) = 10(tan \frac{360 \degree}{2n})(2n)$.
As the regular polygon changes from a pentagon (5 sides) to an octagon (8 sides), what is the approximate average rate of change in the perimeter?

Accepted Answer

decrease of 2.13 inches for each additional side

Answer

decrease of 6.38 inches for each additional side

Answer

decrease of 4.56 inches for each additional side

Answer

decrease of 0.80 inches for each additional side

Question 14

The graph represents the temperature, in degrees Fahrenheit $(\degree F)$, of tea for the first 120 minutes after it was poured into a cup. 
Based on the graph, what was the temperature of the tea when it was first poured into the cup?

Accepted Answer

$204 \degree$

Answer

$114 \degree$

Answer

$68 \degree$

Answer

$136 \degree$

Question 15

The graph represents the temperature, in degrees Fahrenheit $(\degree F)$, of tea for the first 120 minutes after it was poured into a cup. 
Based on the graph, as the number of minutes increased, what temperature did the tea approach?

Accepted Answer

$68 \degree$

Answer

$204 \degree$

Answer

$114 \degree$

Answer

$136 \degree$

Question 16

The population of country $A$ was 40 million in the year 2000 and has grown continually in the years following. The population $P$, in millions, of the country $t$ years after 2000 can be modeled by the function $P(t) = 40e^{0.027t}$, where $t \ge0$.

Based on the model, what was the average rate of change, in millions of people per year, of the population of country $A$ from 2000 to 2005? Give your answer to the nearest hundredth.
Enter your answer in the box.

Accepted Answer

1.16

Question 17

The population of country $A$ was 40 million in the year 2000 and has grown continually in the years following. The population $P$, in millions, of the country $t$ years after 2000 can be modeled by the function $P(t) = 40e^{0.027t}$, where $t \ge0$.

For another country, country $B$, the population $M$, in millions, $t$ years after 2000 can be modeled by the function $M(t) = 35e^{-0.042t}$ t, where $t\ge0$. Based on the models, what year will be the first year in which the population of country $B$ will be greater than the population of country $A$?

Accepted Answer

The population of country $B$ will not exceed the population of country $A$.

Answer

2021

Answer

2009

Answer

2012

Question 18

Select 'each' statement that is true about the graph of $f(x) = sin(x + 3) - 2$.

Accepted Answer

amplitude: 1

Answer

midline: y = 2

Answer

$y$-intercept: (0, -2)

Answer

amplitude: 2

Related quizzes

Related quizzes