Question 1

$$\text { If } f ( x , y , z ) = \frac { x y + z } { x + y z } , \text { calculate the value of } f ( 16.92,2.67 , - 2.76 ) \text {. }$$

Accepted Answer

A)  4.44 
B)  37.64 
C)  -4.86 
D)  44.89 
A)  4.44 
B)  37.64 
C)  -4.86 
D)  44.89 A

Question 2

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 1994.

Accepted Answer

A)  3.61 tons per hectare 
B)  3.71 tons per hectare 
C)  3.75 tons per hectare 
D)  None of the above 
A)  3.61 tons per hectare 
B)  3.71 tons per hectare 
C)  3.75 tons per hectare 
D)  None of the above B

Question 3

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 1992.

Accepted Answer

A)  3.61 tons per hectare 
B)  3.66 tons per hectare 
C)  3.75 tons per hectare 
D)  None of the above 
A)  3.61 tons per hectare 
B)  3.66 tons per hectare 
C)  3.75 tons per hectare 
D)  None of the above B

Question 4

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 56 times per minute.

Accepted Answer

A)  54 degrees 
B)  58 degrees 
C)  40.25 degrees 
D)  none of the above 
A)  54 degrees 
B)  58 degrees 
C)  40.25 degrees 
D)  none of the above

Question 5

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

Accepted Answer

A)  concavity changes 
B)  concavity is at a maximum 
C)  the graph is increasing 
D)  the graph is bent 
A)  concavity changes 
B)  concavity is at a maximum 
C)  the graph is increasing 
D)  the graph is bent

Question 6

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 7

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 8

$$\text { If } f ( x , y ) = \frac { x ^ { \wedge } 3 + y ^ { \wedge } 3 } { x ^ { \wedge } 2 + y ^ { \wedge } 2 } , \text { calculate the value of } f ( 7.44,3.48 ) \text {. }$$

Accepted Answer

A)  6.73 
B)  424.7 
C)  10.92 
D)  None of the above 
A)  6.73 
B)  424.7 
C)  10.92 
D)  None of the above

Question 9

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

Accepted Answer

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

Question 10

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 56 times per minute.

Accepted Answer

A)  54 degrees 
B)  62 degrees 
C)  40.25 degrees 
D)  none of the above 
A)  54 degrees 
B)  62 degrees 
C)  40.25 degrees 
D)  none of the above

Question 11

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 67 times per minute.

Accepted Answer

A)  56.75 degrees 
B)  51 degrees 
C)  40.25 degrees 
D)  none of the above 
A)  56.75 degrees 
B)  51 degrees 
C)  40.25 degrees 
D)  none of the above

Question 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.

Accepted Answer

A)  $\rho \text { oc WV }$ 
B)  $\rho = 46 \mathrm {~W}$ 
C)  $W = 46 P$ 
D)  None of the above. 
A)  $\rho \text { oc WV }$ 
B)  $\rho = 46 \mathrm {~W}$ 
C)  $W = 46 P$ 
D)  None of the above.

Question 13

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 14

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 $V ( 2 )$ .

Accepted Answer

A)  13.6 cubic inches 
B)  15.64 cubic inches 
C)  12.25 cubic inches 
D)  none of the above 
A)  13.6 cubic inches 
B)  15.64 cubic inches 
C)  12.25 cubic inches 
D)  none of the above

Question 15

The temperature of an oven remains constant at 379 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 $D = 304 \times 0.95 ^ { t }$ degrees Fahrenheit. Write a formula that gives the tempera-
Ture $T$ , in degrees Fahrenheit, of the potato after   minutes in the oven.

Accepted Answer

A)  $T = 379 - 304 \times 0.95 ^ { t }$ 
B)  $T = 379 + 304 \times 0.95 ^ { t }$ 
C)  $T = 379 \times 304 \times 0.95 ^ { t }$ 
D)  $T = 304 \times 0.95 ^ { t } - 379$ 
A)  $T = 379 - 304 \times 0.95 ^ { t }$ 
B)  $T = 379 + 304 \times 0.95 ^ { t }$ 
C)  $T = 379 \times 304 \times 0.95 ^ { t }$ 
D)  $T = 304 \times 0.95 ^ { t } - 379$

Question 16

$$\text { If } g ( x , y ) = \frac { e ^ { x } + e ^ { - y } } { x y ^ { - e } } , \text { calculate the value of } g ( 9.3,3.85 )$$

Accepted Answer

A)  10938.02 
B)  45909.64 
C)  45712.3 
D)  -45712.3 
A)  10938.02 
B)  45909.64 
C)  45712.3 
D)  -45712.3

Question 17

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 30 to 40 square miles.

Accepted Answer

A)  1.52 species per square mile 
B)  39 species per square mile 
C)  0.3 species per square mile 
D)  None of the above 
A)  1.52 species per square mile 
B)  39 species per square mile 
C)  0.3 species per square mile 
D)  None of the above

Question 18

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

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

Question 19

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 20

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.

Accepted Answer

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)  $L = 60.8 \times 0.81 ^ { t } - 64$ 
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)  $L = 60.8 \times 0.81 ^ { t } - 64$

$\text { If } f ( x , y , z ) = \frac { x y + z } { x + y z } , \text { calculate the value of } f ( 16.92,2.67 , - 2.76 ) \text {. }$

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

$\text { If } f ( x , y ) = \frac { x ^ { \wedge } 3 + y ^ { \wedge } 3 } { x ^ { \wedge } 2 + y ^ { \wedge } 2 } , \text { calculate the value of } f ( 7.44,3.48 ) \text {. }$

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

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.

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

$\text { If } g ( x , y ) = \frac { e ^ { x } + e ^ { - y } } { x y ^ { - e } } , \text { calculate the value of } g ( 9.3,3.85 )$

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.

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

Graphical and Tabular Analysi

Straight Lines and Linear Functions

Exponential Functions

Filters

Exam 1: Functions

If f(x,y,z)=xy+zx+yz, calculate the value of f(16.92,2.67,−2.76). \text { If } f ( x , y , z ) = \frac { x y + z } { x + y z } , \text { calculate the value of } f ( 16.92,2.67 , - 2.76 ) \text {. } If f(x,y,z)=x+yzxy+z​, calculate the value of f(16.92,2.67,−2.76).

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 1994.

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 1992.

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

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

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.

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

If g(x,y)=ex+e−yxy−e, calculate the value of g(9.3,3.85)\text { If } g ( x , y ) = \frac { e ^ { x } + e ^ { - y } } { x y ^ { - e } } , \text { calculate the value of } g ( 9.3,3.85 ) If g(x,y)=xy−eex+e−y​, calculate the value of g(9.3,3.85)

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.

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.

Graphical and Tabular Analysi

Straight Lines and Linear Functions

Exponential Functions

Filters

$\text { If } f ( x , y , z ) = \frac { x y + z } { x + y z } , \text { calculate the value of } f ( 16.92,2.67 , - 2.76 ) \text {. }$

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.

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

$\text { If } g ( x , y ) = \frac { e ^ { x } + e ^ { - y } } { x y ^ { - e } } , \text { calculate the value of } g ( 9.3,3.85 )$

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