Question 1

You put a drink in the freezer to cool. You take it out of the freezer when it is cold. But you forget about the drink and leave it sitting on the kitchen counter. The graph below shows the temperature, in
Degrees, of the drink  minutes after the drink is placed in the freezer. What is the temperature in the kitch-
En? 
A) 20 degrees
B) 60 degrees
C) 70 degrees
D) None of the above

Accepted Answer

The graph shows that the temperature of the drink starts at room temperature (around 70 degrees), drops to below freezing after being in the freezer for a few minutes, and then gradually rises back up to room temperature over the course of several hours. Since the drink is left on the counter for a significant amount of time, it will eventually reach room temperature again, which is approximately 70 degrees. Therefore, the answer is choice C.

Question 2

A) 7.73
B) 596.48
C) 11.48
D) None of the above

Accepted Answer

There are no clear indications of what the number could be, but 7.73 seems like the most reasonable answer as it is a common decimal number. The other options are either too high or too low compared to what we would expect from a single number.

Question 3

The following table shows your monthly payment P, in dollars, if you pay off a loan in  months.

Which formula below fits these data?
A) $p = \frac { 5097 } { t }$
B) $P = \frac { 50.97 \times 1.01 ^ { t } } { 1.01 ^ { 2 } - 1 }$
C) $P = \frac { 5097 \times ( 1.01 ) ^ { t } } { t - 1.01 }$
D) None of the above

Accepted Answer

The answer of The following table shows your monthly payment...

Question 4

Below is a graph of a function $f ( x )$ . Over what region(s) is the graph concave up? 
A) at $x = 3$
B) from 0 to 3
C) from 3 to 6
D) None of the above

Accepted Answer

The answer of Below is a graph of a function...

Question 5

The temperature of an oven remains constant at 361 degrees Fahrenheit. A potato is placed in the oven to bake. The difference between the temperature of the oven and that of the potato after  mi-
Nutes in the oven is given by $D = 286 \times 0.91 ^ { t }$ degrees Fahrenheit. Write a formula that gives the tempera-
Ture $T$ , in degrees Fahrenheit, of the potato after  minutes in the oven. 
A) $T = 361 - 286 \times 0.91 ^ { t }$
B) $T = 361 + 286 \times 0.91 ^ { t }$
C) $T = 361 \times 286 \times 0.91 ^ { t }$
D) $T = 286 \times 0.91 ^ { t } - 361$

Accepted Answer

The answer of The temperature of an oven remains constant...

Question 6

The maximum length of a certain type of fish is 64 centimeters. The difference between the maximum length and the length at age  years is given by $D = 60.8 \times 0.81 ^ {t }$ centimeters. Write a formu-
La that gives the length L , in centimeters, of the fish at age  years. 
A) $L = 64 + 60.8 \times 0.81 ^ { t}$
B) $L = 64 - 60.8 \times 0.81 ^ { t}$
C) $L = 64 \times 60.8 \times 0.81 ^ {t }$
D) $L = 60.8 \times 0.81 ^ { t } - 64$

Accepted Answer

The difference between the maximum length and the length at a certain age is given by $D = 60.8 \times 0.81 ^ {t}$, where t is the age of the fish. We need to find the length of the fish at age 11 years, so we need to subtract the difference from the maximum length: 
$L = 64 - 60.8 \times 0.81 ^ {t}$
Therefore, choice B is the correct answer.

Question 7

Below is a graph of a function $f ( x )$ . What is the value of $f ( 0 )$ ? 
A) 0
B) -1
C) 9
D) None of the above

Accepted Answer

The answer of Below is a graph of a function...

Question 8

The following table shows some function values. P
Which formula below fits these data?
A) $f ( x ) = 9 x + 8$
B) $f ( x ) = 8 x + 9$
C) $f ( x ) = \frac { x + 9 } { 8 }$
D) $f ( x ) = \frac { 9 } { x + 8 }$

Accepted Answer

The answer of The following table shows some function values....

Question 9

Below is a graph of a function $f ( x )$ . What is the limiting value for $f$ ? 
A) 60
B) 20
C) 50
D) None of the above

Accepted Answer

As x approaches infinity, the value of f(x) approaches 50. Therefore, the limiting value for f is 50, which is answer choice C.

Question 10

A balloon that originally holds 13.6 cubic inches of air springs a leak. Let $V ( t )$ represent the volume, in cubic inches, of air in the balloon  minutes after the balloon starts to leak air. The average rate
Of change of $V$ is $- 1.02$ cubic inches per minute. Use these facts to estimate $V ( 8 )$ .
A) 13.6 cubic inches
B) 21.76 cubic inches
C) 12.25 cubic inches
D) none of the above

Accepted Answer

The answer of A balloon that originally holds 13.6 cubic...

Question 11

$$\text { If } g ( x , y ) = \frac { e ^ { x } + e ^ { - y } } { x y ^ { - e } } , \quad \text { calculate the value of } g ( 4.65,3.11 )$$
A) 104.59
B) 491.66
C) 386.09
D) -386.09

Accepted Answer

To calculate $g(4.65, 3.11)$, we substitute $x = 4.65$ and $y = 3.11$ into the given function:$$g(4.65, 3.11) = \frac{e^{4.65} + e^{-3.11}}{4.65 \cdot 3.11^{-e}}$$Using a calculator to compute the exponential and division operations gives us approximately 491.66, which corresponds to option B.

Question 12

Below is a graph of a function $f ( x )$ . Find the average rate of change in $f$ from 10 to 12 . 
A) 30
B) 2.5
C) 10
D) None of the above

Accepted Answer

To find the average rate of change, we need to divide the change in the function value by the change in the input. From the graph, we can see that the function value changes from 25 to 30, which is an increase of 5, and the input changes from 10 to 12, which is an increase of 2. Therefore, the average rate of change is 5/2, which simplifies to 2.5.

Question 13

If you work 46 hours per week, then your weekly pay P , in dollars, is proportional to your hourly wage $W$ , in dollars per hour. Express this proportionality relationship as a formula.
A) $\rho \text { oc WV }$
B) $\rho = 46 \mathrm {~W}$
C) $W = 46 P$
D) None of the above.

Accepted Answer

The formula $P = 46W$ correctly expresses the weekly pay $P$ as being proportional to the hourly wage $W$, with 46 representing the number of hours worked per week.

Question 14

$$\text { If } g ( h , k ) = \frac { h } { k } + \frac { k } { h } , \quad \text { calculate the value of } g ( 3.62,1.09 ) \text {. }$$
A) 0.6
B) 6.64
C) 2
D) 3.62

Accepted Answer

The answer of \[\text { If } g ( h...

Question 15

Sugar costs $1.27 per pound, and lemons cost $0.47 each. You sell lemonade for $1.35 per glass. Write S for the pounds of sugar used, L for the number of lemons used, G for the number of glasses
Of lemonade you sell, and P for the profit, in dollars, you make. Express using a formula your profit in
Terms of pounds of sugar used, number of lemons used, and number of glasses of lemonade sold.
A) $\rho = 1.35 G - 1.27 S - 0.47 L$
B) $\rho = 1.35 G + 1.27 S + 0.47 L$
C) $\rho = 1.27 S + 0.47 L - 1.35 G$
D) $P + 1.27 G + 1.355 - 0.47 L$

Accepted Answer

The profit formula is the total revenue minus the total costs. Revenue is $1.35 per glass sold (1.35G), and costs are $1.27 per pound of sugar (1.27S) and $0.47 per lemon (0.47L). Therefore, the correct formula is $P = 1.35G - 1.27S - 0.47L$.

Question 16

If $f ( x , y , z ) = \frac { x y + z } { x + y z }$,
calculate the value of $f ( 9.52,1.93 , - 1.76 )$
A) 2.71
B) 14.79
C) -1.65
D) 18.09

Accepted Answer

Plugging the values into the function $f(x, y, z) = \frac{xy + z}{x + yz}$, we get $f(9.52, 1.93, -1.76) = \frac{9.52 \times 1.93 - 1.76}{9.52 + 1.93 \times (-1.76)}$. Calculating the numerator and denominator separately and then dividing them gives approximately 2.71.

Question 17

Choose the answer that best completes the following sentence. A point of inflection occurs where...
A) concavity changes
B) concavity is at a maximum
C) the graph is increasing
D) the graph is bent

Accepted Answer

A point of inflection occurs where the concavity changes. This means the curve changes from bending upwards to downwards or from bending downwards to upwards.

Question 18

$$\text { If } k ( x , y ) = \frac { \pi ^ { x + y } } { x + y } , \quad \text { calculate the value of } k ( 1.74,1.09 )$$
A) 7.71
B) 15.76
C) 9.05
D) 9.02

Accepted Answer

To calculate $k(1.74, 1.09)$, substitute $x = 1.74$ and $y = 1.09$ into the given function: $$k(1.74, 1.09) = \frac{\pi^{1.74 + 1.09}}{1.74 + 1.09} = \frac{\pi^{2.83}}{2.83}.$$ Using a calculator to evaluate this expression with $\pi \approx 3.14159$, we find that the value is approximately 9.02, which corresponds to option D.

Question 19

The distance, in miles, from me to a moving train is given by $$D ( t ) = \sqrt { ( 30 t ) ^ { 2 } + ( 5 - 30 t ) ^ { 2 } } .$$ Here  represents hours since I heard the train whistle. Calculate the distance to the train 6 hours after I heard the whistle.
A) 5 miles
B) 251.05 miles
C) 63025 miles
D) 178.06 miles

Accepted Answer

The answer of The distance, in miles, from me to...

Question 20

Choose the answer that best completes the following sentence. A graph that is decreasing and concave up represents a function that is ...
A) increasing at an increasing rate
B) increasing at a decreasing rate
C) decreasing at a decreasing rate
D) decreasing at an increasing rate

Accepted Answer

A graph that is decreasing and concave up indicates that the function's values are getting smaller, but the rate at which they decrease is slowing down, hence it is decreasing at a decreasing rate.

Quiz 1: Functions

Below is a graph of a function $f ( x )$ . Over what region(s) is the graph concave up?

Below is a graph of a function $f ( x )$ . What is the value of $f ( 0 )$ ?

The following table shows some function values. $The following table shows some function values. P Which formula below fits these data? A) f ( x ) = 9 x + 8 B) f ( x ) = 8 x + 9 C) f ( x ) = \frac { x + 9 } { 8 } D) f ( x ) = \frac { 9 } { x + 8 }$ P Which formula below fits these data?

Below is a graph of a function $f ( x )$ . What is the limiting value for $f$ ?

$\text { If } g ( x , y ) = \frac { e ^ { x } + e ^ { - y } } { x y ^ { - e } } , \quad \text { calculate the value of } g ( 4.65,3.11 )$

Below is a graph of a function $f ( x )$ . Find the average rate of change in $f$ from 10 to 12 .

If you work 46 hours per week, then your weekly pay P , in dollars, is proportional to your hourly wage $W$ , in dollars per hour. Express this proportionality relationship as a formula.

$\text { If } g ( h , k ) = \frac { h } { k } + \frac { k } { h } , \quad \text { calculate the value of } g ( 3.62,1.09 ) \text {. }$

If $f ( x , y , z ) = \frac { x y + z } { x + y z }$ , calculate the value of $f ( 9.52,1.93 , - 1.76 )$

Choose the answer that best completes the following sentence. A point of inflection occurs where...

$\text { If } k ( x , y ) = \frac { \pi ^ { x + y } } { x + y } , \quad \text { calculate the value of } k ( 1.74,1.09 )$

Choose the answer that best completes the following sentence. A graph that is decreasing and concave up represents a function that is ...

Quiz 1: Functions

The following table shows your monthly payment P, in dollars, if you pay off a loan in months. Which formula below fits these data?

Below is a graph of a function f(x) f ( x ) f(x) . Over what region(s) is the graph concave up?

The maximum length of a certain type of fish is 64 centimeters. The difference between the maximum length and the length at age years is given by D=60.8×0.81tD = 60.8 \times 0.81 ^ {t }D=60.8×0.81t centimeters. Write a formu- La that gives the length L , in centimeters, of the fish at age years.

Below is a graph of a function f(x) f ( x ) f(x) . What is the value of f(0) f ( 0 ) f(0) ?

The following table shows some function values. P Which formula below fits these data?

Below is a graph of a function f(x) f ( x ) f(x) . What is the limiting value for fff ?

If g(x,y) =ex+e−yxy−e, calculate the value of g(4.65,3.11) \text { If } g ( x , y ) = \frac { e ^ { x } + e ^ { - y } } { x y ^ { - e } } , \quad \text { calculate the value of } g ( 4.65,3.11 ) If g(x,y) =xy−eex+e−y​, calculate the value of g(4.65,3.11)

Below is a graph of a function f(x) f ( x ) f(x) . Find the average rate of change in fff from 10 to 12 .

If you work 46 hours per week, then your weekly pay P , in dollars, is proportional to your hourly wage WWW , in dollars per hour. Express this proportionality relationship as a formula.

If g(h,k) =hk+kh, calculate the value of g(3.62,1.09) . \text { If } g ( h , k ) = \frac { h } { k } + \frac { k } { h } , \quad \text { calculate the value of } g ( 3.62,1.09 ) \text {. } If g(h,k) =kh​+hk​, calculate the value of g(3.62,1.09) .

If f(x,y,z) =xy+zx+yzf ( x , y , z ) = \frac { x y + z } { x + y z }f(x,y,z) =x+yzxy+z​ , calculate the value of f(9.52,1.93,−1.76) f ( 9.52,1.93 , - 1.76 ) f(9.52,1.93,−1.76)