Question 1

Solve the problem.
-Use the graph of $f$ to estimate the local maximum and local minimum.

Accepted Answer

A)  Local maximum: 1; local minimum: $- 1$ 
B)  Local maximum: 1 ; local minimum: approx. 0 and $- 1$ 
C)  Local maximum: 0 and approx 1 ; local minimum: $- 1$ 
D)  Local maximum: 0; local minimum: $- 1$

Question 2

Match the equation with the appropriate graph.
-$$f ( x ) = \frac { 6 } { x ^ { 2 } + 1 }$$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 3

Solve the problem.
-On a recent trip, Sarah's car traveled 20 mph faster on the first 200 miles than it did on the remaining 80 miles. The total time for the trip was 4 hr. Find the speed of Sarah's car on the first part of the trip.

Accepted Answer

A)  68 mph 
B)  57 mph 
C)  77 mph 
D)  13 mph

Question 4

Determine if the function is one-to-one.
-

Accepted Answer

A) True 
 B)False

Question 5

Write the word or phrase that best completes each statement or answers the question.
Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.
-$$f ( x ) = x ^ { 2 } - 7 \text { and } g ( x ) = \sqrt { 7 + x }$$

Accepted Answer

The answer of Write the word or phrase that best...

Question 6

Determine the intervals on which the function is increasing, decreasing, and constant.
-

Accepted Answer

A)  Increasing on $( - \infty , - 2 )$; Decreasing on $( - \infty , - 2 )$ 
B)  Increasing on $( - \infty , - 2 )$; Decreasing on $( - 2 , \infty )$ 
C)  Increasing on $( - 2 , \infty )$; Decreasing on $( - \infty , - 2 )$ 
D)  Increasing on $( - 2 , \infty )$; Decreasing on $( - 2 \infty )$

Question 7

Determine algebraically whether the function is even, odd, or neither even nor odd.
-$$f ( x ) = \sqrt { x ^ { 2 } + 6 }$$

Accepted Answer

A)  Odd 
B)  Even 
C)  Neither

Question 8

Identify intervals on which the function is increasing, decreasing, or constant.
-$$f ( x ) = x ^ { 3 } - x ^ { 2 } + 2$$

Accepted Answer

A)  Increasing: $( - \infty , 0 )$ and $( 0.67 , \infty )$; decreasing: $( 0,0.67 )$ 
B)  Increasing: $( 0,0.67 )$; decreasing: $( - \infty , 0 )$ and $( 0.67 , \infty )$ 
C)  Increasing: $( - \infty , - 2 )$ and $( 2 , \infty )$; decreasing: $( - 2,2 )$ 
D)  Increasing: $( - \infty , 0 )$ and $( 0.67 , \infty )$; constant: $( 0,0.67 )$

Question 9

Sketch the graph of y1 as a solid line or curve. Then sketch the graph of y2 as a dashed line or curve by one or more of
these: a vertical and/or horizontal shift of the graph y1, a vertical stretch or shrink of the graph of y1, or a reflection of the
graph of y1 across an axis.
-$y_{1}=x^{2} ; y_{2}=x^{2}-4$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 10

Match the numerical model to the corresponding model.
-$\begin{array}{r|rrrrrr}
\mathrm{x} & 0 & 1 & 2 & 3 & 4 & 5 \
\hline \mathrm{y} & 25 & 22 & 19 & 16 & 13 & 10
\end{array}$

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 11

Graph the inverse of the function plotted, on the same set of axes. Use a dashed curve for the inverse.
-

Accepted Answer

A) 
 
B) 
 
C) 
 
D)

Question 12

Choose the one alternative that best completes the statement or answers the question.
Write a mathematical expression for the quantity described verbally.
-The area of a triangle whose altitude is 8 more than its base length $x$

Accepted Answer

A)  $\frac { 1 } { 2 } ( x ) ( x - 8 )$ 
B)  $( x ) ( x + 8 )$ 
C)  $\frac { 1 } { 2 } ( x ) ( x + 8 )$ 
D)  $\frac { 1 } { 2 } x ^ { 2 } - 8$

Question 13

Write the word or phrase that best completes each statement or answers the question.
Sketch the graph of the given function based on the graph of the function f given below.
-$$\text { Sketch the graph of } y = 2 f ( x + 1 ) \text {. }$$

Accepted Answer

The answer of Write the word or phrase that best...

Question 14

Determine the intervals on which the function is increasing, decreasing, and constant.
-

Accepted Answer

A)  Increasing on $( - \infty , 0 )$; Decreasing on $( - \infty , 0 )$ 
B)  Increasing on $( 0 , \infty )$; Decreasing on $( - \infty , 0 )$ 
C)  Increasing on $( - \infty , 0 )$; Decreasing on $( 0 , \infty )$ 
D)  Increasing on $( \infty , 0 )$; Decreasing on $( 0 , - \infty )$

Question 15

Determine the intervals on which the function is increasing, decreasing, and constant.
-

Accepted Answer

A)  Increasing on $( 0 , \infty )$; Decreasing on $( - \infty , 0 )$ 
B)  Increasing on $( - \infty , \infty )$ 
C)  Decreasing on $( - \infty , \infty )$ 
D)  Increasing on $( - \infty , 0 )$; Decreasing on $( 0 , \infty )$

Question 16

Match the numerical model to the corresponding model.
-$\begin{array}{l|rrrrrr}
\mathrm{x} & 2 & 4 & 6 & 8 & 10 & 12 \
\hline \mathrm{y} & 10 & 20 & 30 & 40 & 50 & 60
\end{array}$

Accepted Answer

A)  $y = \frac { 1 } { 5 } x$ 
B)  $y = x + 5$ 
C)  $y = 5 x + 1$ 
D)  $y = 5 x$

Question 17

Match the numerical model to the corresponding model.
-$\begin{array}{r|rrrrrr}
\mathrm{x} & 0 & 1 & 2 & 3 & 4 & 5 \
\hline \mathrm{y} & 60 & 58 & 52 & 42 & 28 & 10
\end{array}$

Accepted Answer

A)  $y = 60 - 2 x ^ { 2 }$ 
B)  $y = 60 - 2 x$ 
C)  $y = x + 60$ 
D)  $y = 60 - x ^ { 2 }$

Question 18

Write the word or phrase that best completes each statement or answers the question.
Graph the function on your calculator in order to answer the following questions:
On what intervals is the function increasing? decreasing?
Is the function odd, even, or neither?
Give the function's extrema, if any.
Find the horizontal asymptotes, if any.
How does the graph relate to a graph of one of the twelve basic functions?
-$$f ( x ) = 4 | x |$$

Accepted Answer

The answer of Write the word or phrase that best...

Question 19

Identify which of the twelve basic functions listed below fit the description given.
-The four functions that are increasing on the interval $( - \infty , 0 )$

Accepted Answer

A)  $y = x , y = x ^ { 3 } , y = x ^ { 2 } , y = e ^ { x }$ 
B)  $y = x , y = x ^ { 3 } , y = e ^ { x } , y = \frac { 1 } { 1 + e ^ { - x } }$ 
C)  $y = x , y = x ^ { 3 } , y = x ^ { 2 } , y = \frac { 1 } { 1 + e ^ { - x } }$ 
D)  $y = x ^ { 3 } , y = \frac { 1 } { x } , y = | x | , y = x$

Question 20

Graph the function and determine if it has a point of discontinuity at x = 0. If there is a discontinuity, tell whether it is
removable or non-removable.
-$$h ( x ) = \frac { x } { x - 2 }$$

Accepted Answer

A)

Yes; non-removable 
B)

Yes; non-removable 
C)

No 
D)

No

Exam 1: Functions and Graphs

Solve the problem. -Use the graph of $f$ to estimate the local maximum and local minimum.

Match the equation with the appropriate graph. - $f ( x ) = \frac { 6 } { x ^ { 2 } + 1 }$

Solve the problem. -On a recent trip, Sarah's car traveled 20 mph faster on the first 200 miles than it did on the remaining 80 miles. The total time for the trip was 4 hr. Find the speed of Sarah's car on the first part of the trip.

Determine if the function is one-to-one. -

Write the word or phrase that best completes each statement or answers the question. Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. - $f ( x ) = x ^ { 2 } - 7 \text { and } g ( x ) = \sqrt { 7 + x }$

Determine algebraically whether the function is even, odd, or neither even nor odd. - $f ( x ) = \sqrt { x ^ { 2 } + 6 }$

Identify intervals on which the function is increasing, decreasing, or constant. - $f ( x ) = x ^ { 3 } - x ^ { 2 } + 2$

Match the numerical model to the corresponding model. - $\begin{array}{r|rrrrrr}\mathrm{x} & 0 & 1 & 2 & 3 & 4 & 5 \\\hline \mathrm{y} & 25 & 22 & 19 & 16 & 13 & 10\end{array}$

Graph the inverse of the function plotted, on the same set of axes. Use a dashed curve for the inverse. -

Choose the one alternative that best completes the statement or answers the question. Write a mathematical expression for the quantity described verbally. -The area of a triangle whose altitude is 8 more than its base length $x$

Match the numerical model to the corresponding model. - $\begin{array}{l|rrrrrr}\mathrm{x} & 2 & 4 & 6 & 8 & 10 & 12 \\\hline \mathrm{y} & 10 & 20 & 30 & 40 & 50 & 60\end{array}$

Match the numerical model to the corresponding model. - $\begin{array}{r|rrrrrr}\mathrm{x} & 0 & 1 & 2 & 3 & 4 & 5 \\\hline \mathrm{y} & 60 & 58 & 52 & 42 & 28 & 10\end{array}$

Identify which of the twelve basic functions listed below fit the description given. -The four functions that are increasing on the interval $( - \infty , 0 )$

Exam 1: Functions and Graphs

Solve the problem. -Use the graph of fff to estimate the local maximum and local minimum.

Match the equation with the appropriate graph. - f(x) =6x2+1f ( x ) = \frac { 6 } { x ^ { 2 } + 1 }f(x) =x2+16​

Solve the problem. -On a recent trip, Sarah's car traveled 20 mph faster on the first 200 miles than it did on the remaining 80 miles. The total time for the trip was 4 hr. Find the speed of Sarah's car on the first part of the trip.

Determine if the function is one-to-one. -

Write the word or phrase that best completes each statement or answers the question. Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. - f(x)=x2−7 and g(x)=7+xf ( x ) = x ^ { 2 } - 7 \text { and } g ( x ) = \sqrt { 7 + x }f(x)=x2−7 and g(x)=7+x​

Determine the intervals on which the function is increasing, decreasing, and constant. -

Determine algebraically whether the function is even, odd, or neither even nor odd. - f(x) =x2+6f ( x ) = \sqrt { x ^ { 2 } + 6 }f(x) =x2+6​

Identify intervals on which the function is increasing, decreasing, or constant. - f(x) =x3−x2+2f ( x ) = x ^ { 3 } - x ^ { 2 } + 2f(x) =x3−x2+2

Match the numerical model to the corresponding model. - x012345y252219161310\begin{array}{r|rrrrrr}\mathrm{x} & 0 & 1 & 2 & 3 & 4 & 5 \\\hline \mathrm{y} & 25 & 22 & 19 & 16 & 13 & 10\end{array}xy​025​122​219​316​413​510​​

Graph the inverse of the function plotted, on the same set of axes. Use a dashed curve for the inverse. -

Choose the one alternative that best completes the statement or answers the question. Write a mathematical expression for the quantity described verbally. -The area of a triangle whose altitude is 8 more than its base length xxx

Write the word or phrase that best completes each statement or answers the question. Sketch the graph of the given function based on the graph of the function f given below. - Sketch the graph of y=2f(x+1). \text { Sketch the graph of } y = 2 f ( x + 1 ) \text {. } Sketch the graph of y=2f(x+1).

Determine the intervals on which the function is increasing, decreasing, and constant. -

Determine the intervals on which the function is increasing, decreasing, and constant. -

Match the numerical model to the corresponding model. - x24681012y102030405060\begin{array}{l|rrrrrr}\mathrm{x} & 2 & 4 & 6 & 8 & 10 & 12 \\\hline \mathrm{y} & 10 & 20 & 30 & 40 & 50 & 60\end{array}xy​210​420​630​840​1050​1260​​

Match the numerical model to the corresponding model. - x012345y605852422810\begin{array}{r|rrrrrr}\mathrm{x} & 0 & 1 & 2 & 3 & 4 & 5 \\\hline \mathrm{y} & 60 & 58 & 52 & 42 & 28 & 10\end{array}xy​060​158​252​342​428​510​​

Identify which of the twelve basic functions listed below fit the description given. -The four functions that are increasing on the interval (−∞,0) ( - \infty , 0 ) (−∞,0)

Graph the function and determine if it has a point of discontinuity at x = 0. If there is a discontinuity, tell whether it is removable or non-removable. - h(x) =xx−2h ( x ) = \frac { x } { x - 2 }h(x) =x−2x​

Solve the problem. -Use the graph of $f$ to estimate the local maximum and local minimum.

Match the equation with the appropriate graph. - $f ( x ) = \frac { 6 } { x ^ { 2 } + 1 }$

Write the word or phrase that best completes each statement or answers the question. Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. - $f ( x ) = x ^ { 2 } - 7 \text { and } g ( x ) = \sqrt { 7 + x }$

Determine algebraically whether the function is even, odd, or neither even nor odd. - $f ( x ) = \sqrt { x ^ { 2 } + 6 }$

Identify intervals on which the function is increasing, decreasing, or constant. - $f ( x ) = x ^ { 3 } - x ^ { 2 } + 2$

Match the numerical model to the corresponding model. - $\begin{array}{r|rrrrrr}\mathrm{x} & 0 & 1 & 2 & 3 & 4 & 5 \\\hline \mathrm{y} & 25 & 22 & 19 & 16 & 13 & 10\end{array}$

Choose the one alternative that best completes the statement or answers the question. Write a mathematical expression for the quantity described verbally. -The area of a triangle whose altitude is 8 more than its base length $x$

Match the numerical model to the corresponding model. - $\begin{array}{l|rrrrrr}\mathrm{x} & 2 & 4 & 6 & 8 & 10 & 12 \\\hline \mathrm{y} & 10 & 20 & 30 & 40 & 50 & 60\end{array}$

Match the numerical model to the corresponding model. - $\begin{array}{r|rrrrrr}\mathrm{x} & 0 & 1 & 2 & 3 & 4 & 5 \\\hline \mathrm{y} & 60 & 58 & 52 & 42 & 28 & 10\end{array}$

Identify which of the twelve basic functions listed below fit the description given. -The four functions that are increasing on the interval $( - \infty , 0 )$