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 1994.

A) 261.79 million B) 251.98 million C) 265.07 million D) None of the above A) 261.79 million B) 251.98 million C) 265.07 million D) None of the above

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 1992.

A) 255.25 million B) 251.98 million C) 265.07 million D) None of the above A) 255.25 million B) 251.98 million C) 265.07 million D) None of the above

Exam 1: Functions

The following table shows average rice yield, in tons per hectare, in Asia $The following table shows average rice yield, in tons per hectare, in Asia years since 1980. \begin{array} { | l | l | l | l | l | l | } \hline \begin{array} { l } \text { t=years since } \\ 1980 \end{array} & 5 & 10 & 15 & 20 & 25 \\ \hline Y = \text { yield } & 3.32 & 3.61 & 3.73 & 3.95 & 4.11 \\ \hline \end{array} Use the average rate of change to estimate the yield in 1993.$ 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 1993.

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Question 81

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

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Question 82

(Multiple Choice)

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Question 83

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

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Question 84

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

(Multiple Choice)

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Question 85

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

(Multiple Choice)

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Question 86

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 1994.

(Multiple Choice)

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Question 87

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

(Multiple Choice)

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Question 88

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

(Multiple Choice)

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Question 89

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 1992.

(Multiple Choice)

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Question 90

$\text { If } f ( x , y ) = \frac { x ^ { \wedge } 3 + y ^ { \wedge } 3 } { x ^ { \wedge } 2 + y ^ { \wedge } 2 } , \text { calculate the value of } f ( 7.44,2.37 ) \text {. }$

(Multiple Choice)

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Question 91

If you work 45 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.

(Multiple Choice)

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Question 92

If $g ( h , k ) = \frac { h } { k } + \frac { k } { h }$ , calculate the value of $g ( 5.03,1.41 )$ .

(Multiple Choice)

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Question 93

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 $V ( 7 )$ .

(Multiple Choice)

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Question 94

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

(Multiple Choice)

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Question 95

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

(Multiple Choice)

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Question 96

Below is a graph of a function $f ( x )$ . Find the average rate of change in $f$ from 2 to 4 .

(Multiple Choice)

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Question 97

Below is a graph of a function $f ( x )$ . Find the average rate of change in $f$ from 2 to 4 .

(Multiple Choice)

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Question 98

If $f ( x , y , z ) = \frac { x y + z } { x + y z }$ , calculate the value of $f ( 16.92,1.56 , - 3.76 )$

(Multiple Choice)

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Question 99

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

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

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

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

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 1994.

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

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

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 1992.

$\text { If } f ( x , y ) = \frac { x ^ { \wedge } 3 + y ^ { \wedge } 3 } { x ^ { \wedge } 2 + y ^ { \wedge } 2 } , \text { calculate the value of } f ( 7.44,2.37 ) \text {. }$

If you work 45 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.

If $g ( h , k ) = \frac { h } { k } + \frac { k } { h }$ , calculate the value of $g ( 5.03,1.41 )$ .

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

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

Below is a graph of a function $f ( x )$ . Find the average rate of change in $f$ from 2 to 4 .

Below is a graph of a function $f ( x )$ . Find the average rate of change in $f$ from 2 to 4 .

If $f ( x , y , z ) = \frac { x y + z } { x + y z }$ , calculate the value of $f ( 16.92,1.56 , - 3.76 )$

Graphical and Tabular Analysi

Straight Lines and Linear Functions

Exponential Functions

Filters

Exam 1: Functions

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 1993.

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

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

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

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 .

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 1994.

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

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)

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 1992.

If you work 45 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+khg ( h , k ) = \frac { h } { k } + \frac { k } { h }g(h,k)=kh​+hk​ , calculate the value of g(5.03,1.41)g ( 5.03,1.41 )g(5.03,1.41) .

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

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

Below is a graph of a function f(x)f ( x )f(x) . Find the average rate of change in fff from 2 to 4 .

Below is a graph of a function f(x)f ( x )f(x) . Find the average rate of change in fff from 2 to 4 .

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(16.92,1.56,−3.76)f ( 16.92,1.56 , - 3.76 )f(16.92,1.56,−3.76)

Graphical and Tabular Analysi

Straight Lines and Linear Functions

Exponential Functions

Filters

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

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 $f ( x )$ . Find the average rate of change in $f$ from 10 to 12 .

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

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

If you work 45 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.

If $g ( h , k ) = \frac { h } { k } + \frac { k } { h }$ , calculate the value of $g ( 5.03,1.41 )$ .

Below is a graph of a function $f ( x )$ . Find the average rate of change in $f$ from 2 to 4 .

Below is a graph of a function $f ( x )$ . Find the average rate of change in $f$ from 2 to 4 .

If $f ( x , y , z ) = \frac { x y + z } { x + y z }$ , calculate the value of $f ( 16.92,1.56 , - 3.76 )$