Question 1

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

Accepted Answer

A)  increasing at a decreasing rate 
B)  increasing at an increasing rate 
C)  decreasing at an increasing rate 
D)  decreasing at a decreasing rate 
A)  increasing at a decreasing rate 
B)  increasing at an increasing rate 
C)  decreasing at an increasing rate 
D)  decreasing at a decreasing rate

Question 2

The maximum length of a certain type of fish is 63 centimeters. The difference between the maximum length and the length at age   years is given by $D = 59.85 \times 0.83 ^ { t }$ centimeters. Write a for-
Mula that gives the length L , in centimeters, of the fish at age   years.

Accepted Answer

A)  $L = 63 + 59.85 \times 0.83 ^ { t }$ 
B)  $L = 63 - 59.85 \times 0.83 ^ { t}$ 
C)  $L = 63 \times 59.85 \times 0.83 ^ { t }$ 
D)  $L = 59.85 \times 0.83 ^ { t } - 63$ 
A)  $L = 63 + 59.85 \times 0.83 ^ { t }$ 
B)  $L = 63 - 59.85 \times 0.83 ^ { t}$ 
C)  $L = 63 \times 59.85 \times 0.83 ^ { t }$ 
D)  $L = 59.85 \times 0.83 ^ { t } - 63$

Question 3

Below is a graph of a function $f ( x )$ . What is the value of $f ( 4 )$ ?

Accepted Answer

A)  8 
B)  -8 
C)  9 
D)  None of the above 
A)  8 
B)  -8 
C)  9 
D)  None of the above

Question 4

The following table shows average rice yield, in tons per hectare, in Asia   years since 1980. $$\begin{array} { | l | l | l | l | l | l | } 
\hline \begin{array} { l } 
\text { t=years since } \
1980
\end{array} & 5 & 10 & 15 & 20 & 25 \
\hline Y = \text { yield } & 3.32 & 3.61 & 3.73 & 3.95 & 4.11 \
\hline
\end{array}$$ Use the average rate of change to estimate the yield in 1999.

Accepted Answer

A)  3.73 tons per hectare 
B)  3.91 tons per hectare 
C)  3.87 tons per hectare 
D)  None of the above 
A)  3.73 tons per hectare 
B)  3.91 tons per hectare 
C)  3.87 tons per hectare 
D)  None of the above

Question 5

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?

Accepted Answer

A)  20 degrees 
B)  60 degrees 
C)  70 degrees 
D)  None of the above 
A)  20 degrees 
B)  60 degrees 
C)  70 degrees 
D)  None of the above

Question 6

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

Accepted Answer

A)  0.6 
B)  6.64 
C)  2 
D)  3.62 
A)  0.6 
B)  6.64 
C)  2 
D)  3.62

Question 7

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 5 hours after I heard the whistle.

Accepted Answer

A)  5 miles 
B)  208.63 miles 
C)  43525 miles 
D)  147.56 miles 
A)  5 miles 
B)  208.63 miles 
C)  43525 miles 
D)  147.56 miles

Question 8

Below is a graph of a function $f ( x )$ . Find the average rate of change in $f$ from 4 to 10 .

Accepted Answer

A)  20 
B)  -5 
C)  -30 
D)  None of the above 
A)  20 
B)  -5 
C)  -30 
D)  None of the above

Question 9

The following table shows some function values.

Which formula below fits these data?

Accepted Answer

A)  $f ( x ) = 7 x + 5$ 
B)  $f ( x ) = 5 x + 7$ 
C)  $f ( x ) = \frac { x + 7 } { 5 }$ 
D)  $f ( x ) = \frac { 7 } { x + 5 }$ 
A)  $f ( x ) = 7 x + 5$ 
B)  $f ( x ) = 5 x + 7$ 
C)  $f ( x ) = \frac { x + 7 } { 5 }$ 
D)  $f ( x ) = \frac { 7 } { x + 5 }$

Question 10

Accepted Answer

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

Question 11

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.

Accepted Answer

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)  $P + 1.27 G + 1.355 - 0.47 L$ 
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)  $P + 1.27 G + 1.355 - 0.47 L$

Question 12

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

Accepted Answer

A)  $p=\frac{5021}{t}$ 
B)  $P=\frac{50.21 \times 1.01^{2}}{1.01^{2}-1}$ 
C)  $P=\frac{5021 \times(1.01)^{2}}{t-1.01}$ 
D)  None of the above 
A)  $p=\frac{5021}{t}$ 
B)  $P=\frac{50.21 \times 1.01^{2}}{1.01^{2}-1}$ 
C)  $P=\frac{5021 \times(1.01)^{2}}{t-1.01}$ 
D)  None of the above

Question 13

Sugar costs $1.62 per pound, and lemons cost $0.64 each. You sell lemonade for $1.75 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.

Accepted Answer

A)  $P = 1.75 G - 1.62 S - 0.64 L$ 
B)  $P = 1.75 G + 1.62 S + 0.64 L$ 
C)  $P = 1.62 S + 0.64 L - 1.75 G$ 
D)  $P + 1.62 G + 1.75 S - 0.64 L$ 
A)  $P = 1.75 G - 1.62 S - 0.64 L$ 
B)  $P = 1.75 G + 1.62 S + 0.64 L$ 
C)  $P = 1.62 S + 0.64 L - 1.75 G$ 
D)  $P + 1.62 G + 1.75 S - 0.64 L$

Question 14

The temperature in degrees Fahrenheit can be estimated from the number of cricket chirps per minute. If a cricket chirps 40 times per minute, the temperature is approximately 50 degrees Fahrenheit.
The average rate of change in temperature is 0.25 degree per chirp per minute. Use these facts to estimate
The temperature when a cricket chirps 51 times per minute.

Accepted Answer

A)  52.75 degrees 
B)  78 degrees 
C)  40.25 degrees 
D)  none of the above 
A)  52.75 degrees 
B)  78 degrees 
C)  40.25 degrees 
D)  none of the above

Question 15

The following table shows the number of bird species found on an island of area $A$ square miles that is part of a particular Pacific island chain. $$\begin{array} { | l | l | l | l | l | l | } 
\hline A = \text { area } & 10 & 20 & 30 & 40 & 50 \
\hline \begin{array} { l } 
W = \text { number } \
\text { of species }
\end{array} & 25 & 31 & 36 & 39 & 42 \
\hline
\end{array}$$ Calculate the average rate of change in the number of species as the area changes from 10 to 20 square miles.

Accepted Answer

A)  1.52 species per square mile 
B)  31 species per square mile 
C)  0.6 species per square mile 
D)  None of the above 
A)  1.52 species per square mile 
B)  31 species per square mile 
C)  0.6 species per square mile 
D)  None of the above

Question 16

$$\text { If } f ( x , y , z ) = \frac { x y + z } { x + y z } , \text { calculate the value of } f ( 9.52,3.04 , - 2.76 )$$

Accepted Answer

A)  23.18 
B)  20.26 
C)  -5.64 
D)  26.5 
A)  23.18 
B)  20.26 
C)  -5.64 
D)  26.5

Question 17

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 $V ( 6 )$ .

Accepted Answer

A)  13.6 cubic inches 
B)  19.72 cubic inches 
C)  12.93 cubic inches 
D)  none of the above 
A)  13.6 cubic inches 
B)  19.72 cubic inches 
C)  12.93 cubic inches 
D)  none of the above

Question 18

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

Accepted Answer

A)  at $x = 3$ 
B)  from 0 to 3 
C)  from 3 to 6 
D)  None of the above 
A)  at $x = 3$ 
B)  from 0 to 3 
C)  from 3 to 6 
D)  None of the above

Question 19

Sugar costs $1.62 per pound, and lemons cost $0.64 each. You sell lemonade for $1.75 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.

Accepted Answer

A)  $P = 1.75 G - 1.62 S - 0.64 L$ 
B)  $\quad P = 1.75 G + 1.62 S + 0.64 L$ 
C)  $P = 1.62 S + 0.64 L - 1.75 G$ 
D)  $P + 1.62 G + 1.75 S - 0.64 L$ 
A)  $P = 1.75 G - 1.62 S - 0.64 L$ 
B)  $\quad P = 1.75 G + 1.62 S + 0.64 L$ 
C)  $P = 1.62 S + 0.64 L - 1.75 G$ 
D)  $P + 1.62 G + 1.75 S - 0.64 L$

Question 20

The following table shows the U.S. population, in millions, in the given year. $$\begin{array} { | l | l | l | l | l | l | } 
\hline d = \text { year } & 1960 & 1970 & 1980 & 1990 & 2000 \
\hline \begin{array} { l } 
N = \text { popula- } \
\text { tion in mil- } \
\text { lions }
\end{array} & 179.32 & 203.3 & 226.54 & 248.71 & 281.42 \
\hline
\end{array}$$ Use the average rate of change to estimate the U.S. population in 1996.

Accepted Answer

A)  268.34 million 
B)  251.98 million 
C)  265.07 million 
D)  None of the above 
A)  268.34 million 
B)  251.98 million 
C)  265.07 million 
D)  None of the above

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

Below is a graph of a function $f ( x )$ . What is the value of $f ( 4 )$ ?

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

Below is a graph of a function $f ( x )$ . Find the average rate of change in $f$ from 4 to 10 .

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

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

$\text { If } f ( x , y , z ) = \frac { x y + z } { x + y z } , \text { calculate the value of } f ( 9.52,3.04 , - 2.76 )$

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

The following table shows the U.S. population, in millions, in the given year. d= year 1960 1970 1980 1990 2000 N= popula- tion in mil- lions 179.32 203.3 226.54 248.71 281.42 Use the average rate of change to estimate the U.S. population in 1996.

Graphical and Tabular Analysi

Straight Lines and Linear Functions

Exponential Functions

Filters

Exam 1: Functions

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

Below is a graph of a function f(x)f ( x )f(x) . What is the value of f(4)f ( 4 )f(4) ?

The following table shows average rice yield, in tons per hectare, in Asia years since 1980. t=years since 1980 5 10 15 20 25 Y= yield 3.32 3.61 3.73 3.95 4.11 Use the average rate of change to estimate the yield in 1999.

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).

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

Below is a graph of a function f(x)f ( x )f(x) . Find the average rate of change in fff from 4 to 10 .

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

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

If f(x,y,z)=xy+zx+yz, calculate the value of f(9.52,3.04,−2.76)\text { If } f ( x , y , z ) = \frac { x y + z } { x + y z } , \text { calculate the value of } f ( 9.52,3.04 , - 2.76 ) If f(x,y,z)=x+yzxy+z​, calculate the value of f(9.52,3.04,−2.76)

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

The following table shows the U.S. population, in millions, in the given year. d= year 1960 1970 1980 1990 2000 N= popula- tion in mil- lions 179.32 203.3 226.54 248.71 281.42 Use the average rate of change to estimate the U.S. population in 1996.

Graphical and Tabular Analysi

Straight Lines and Linear Functions

Exponential Functions

Filters

Below is a graph of a function $f ( x )$ . What is the value of $f ( 4 )$ ?

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

Below is a graph of a function $f ( x )$ . Find the average rate of change in $f$ from 4 to 10 .

$\text { If } f ( x , y , z ) = \frac { x y + z } { x + y z } , \text { calculate the value of } f ( 9.52,3.04 , - 2.76 )$

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