Question 1

Find the average rate of change of the function between the given points $f ( x ) = 2 x ^ { 2 } + x ; \quad x = 0 , x = 2$

Accepted Answer

The answer of Find the average rate of change of...

Question 2

If an object is dropped from a high cliff or a tall building, then the distance it has fallen after t seconds is given by the function $f ( t ) = 16 t ^ { 2 }$ 
Find its average speed (average rate of change) over the following intervals:
(i) Between 1 s and 6 s
(ii) Between $t = c \text { and } t = c + h$

Accepted Answer

The answer of If an object is dropped from a...

Question 3

Evaluate $f ( - 1 )$ , $f ( 0 )$, $f ( 1 )$
, for the piecewise-defined function. $f ( x ) = \left\{ \begin{array} { l l } x ^ { 2 } & \text { if } x < 0 \ x - 1 & \text { if } x \geq 0 \end{array} \right.$

Accepted Answer

A)  $f ( - 1 ) = 1 , f ( 0 ) = - 1 , f ( 1 ) = 0$ 
B)  $f ( - 1 ) = - 2 , f ( 0 ) = 0 , f ( 1 ) = 1$ 
C)  $f ( - 1 ) = - 1 , f ( 0 ) = 0 , f ( 1 ) = 1$ 
D)  $f ( - 1 ) = 2 , f ( 0 ) = 1 , f ( 1 ) = - 3$ 
E)  none of these 
A)  $f ( - 1 ) = 1 , f ( 0 ) = - 1 , f ( 1 ) = 0$ 
B)  $f ( - 1 ) = - 2 , f ( 0 ) = 0 , f ( 1 ) = 1$ 
C)  $f ( - 1 ) = - 1 , f ( 0 ) = 0 , f ( 1 ) = 1$ 
D)  $f ( - 1 ) = 2 , f ( 0 ) = 1 , f ( 1 ) = - 3$ 
E)  none of these

Question 4

A man is running around a circular track that is 200 m in circumference. An observer uses a stopwatch to record the runner's time at the end of each lap, obtaining the data in the following table.What was the man's average speed (rate) between 108 s and 203 s? Round the answer to two decimal places. $$\begin{array} { c c } 
\text { Time (s) } & \begin{array} { c } 
\text { Distance } \
\text { (m) }
\end{array} \
32 & 200 \
68 & 400 \
108 & 600 \
152 & 800 \
203 & 1000 \
263 & 1200 \
335 & 1400 \
412 & 1600
\end{array}$$

Accepted Answer

The answer of A man is running around a circular...

Question 5

Use a graphing calculator to determine approximately the internals on which the function $f$ is decreasing. $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + x ^ { 2 } - 24 x + 16$

Accepted Answer

A)  $[ - 4 , - 1.5 ] , [ 1 , \infty )$ 
B)  $( - \infty , - 4 ] , [ - 1.5,1 )$ 
C)  $( 0 , \infty )$ 
D)  $( 0 , - 16 )$ 
E)  $( - \infty , - 16 ]$ 
A)  $[ - 4 , - 1.5 ] , [ 1 , \infty )$ 
B)  $( - \infty , - 4 ] , [ - 1.5,1 )$ 
C)  $( 0 , \infty )$ 
D)  $( 0 , - 16 )$ 
E)  $( - \infty , - 16 ]$

Question 6

Use a graphing calculator to determine approximately the internals on which the function $f$ is decreasing. $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + x ^ { 2 } - 24 x + 16$

Accepted Answer

A)  $[ - 4 , - 1.5 ] , [ 1 , \infty )$ 
B)  $( - \infty , - 4 ] , [ - 1.5,1 )$ 
C)  $( 0 , \infty )$ 
D)  $( 0 , - 16 )$ 
E)  $( - \infty , - 16 ]$ 
A)  $[ - 4 , - 1.5 ] , [ 1 , \infty )$ 
B)  $( - \infty , - 4 ] , [ - 1.5,1 )$ 
C)  $( 0 , \infty )$ 
D)  $( 0 , - 16 )$ 
E)  $( - \infty , - 16 ]$

Question 7

Determine if the equation $x ^ { 2 } + ( y - 1 ) ^ { 2 } = 36$ defines y as a function of x

Accepted Answer

A)  The equation represents a function because it's a circle 
B)  The equation represents a function because for each value of x there is always two values of y 
C)  Not a function because the equation gives two values of y for a given value of x 
D)  The equation represents a function because it passes the vertical line test 
E)  Not a function because the equation passes the vertical line test. 
A)  The equation represents a function because it's a circle 
B)  The equation represents a function because for each value of x there is always two values of y 
C)  Not a function because the equation gives two values of y for a given value of x 
D)  The equation represents a function because it passes the vertical line test 
E)  Not a function because the equation passes the vertical line test.

Question 8

Find the domain of the function. $f ( x ) = 0.5 x - \frac { 2 } { \sqrt { x + 1 } }$

Accepted Answer

The answer of Find the domain of the function. \(f...

Question 9

Determine whether or not the function $f ( x ) = - 2 x ^ { 2 } + 18 x - 16$ 
is one-to-one.

Accepted Answer

The answer of Determine whether or not the function \(f...

Question 10

Sketch the graph of the piecewise defined function. $$f ( x ) = \left\{ \begin{array} { l l } 
x + 2 & \text { if } x < 0 \
2 & \text { if } 0 \leq x \leq 1 \
3 - x & \text { if } 1 < x
\end{array} \right.$$

Accepted Answer

The answer of Sketch the graph of the piecewise defined...

Question 11

Use a graphing device to draw the graph of the function $f ( x ) = - 3 - 3 x ^ { 2 }$ . State approximately the interval(s) on which the function is increasing and on which the function is decreasing

Accepted Answer

A)  $f$
Is increasing on $( - \infty , 0 ]$
And decreasing on $[ 0 , \infty )$ 
B)  $f$
Is increasing on $( - \infty , - 3 )$
And decreasing on $[ 3 , \infty )$ 
C)  $f$
Is increasing on $( - \infty , \infty )$ 
D)  $f$
Is decreasing on $[ 0 , \infty )$
Only 
E)  none of these 
A)  $f$
Is increasing on $( - \infty , 0 ]$
And decreasing on $[ 0 , \infty )$ 
B)  $f$
Is increasing on $( - \infty , - 3 )$
And decreasing on $[ 3 , \infty )$ 
C)  $f$
Is increasing on $( - \infty , \infty )$ 
D)  $f$
Is decreasing on $[ 0 , \infty )$
Only 
E)  none of these

Question 12

Find the inverse of the function. $f ( x ) = 3 x + 2$

Accepted Answer

The answer of Find the inverse of the function. \(f...

Question 13

Find the inverse of the function. $g ( x ) = x ^ { 2 } - 9 , x \geq 0$

Accepted Answer

The answer of Find the inverse of the function. \(g...

Question 14

Find the inverse of the function. $g ( x ) = x ^ { 2 } - 16 , x \geq 0$

Accepted Answer

A)  $g ^ { - 1 } ( x ) = - \sqrt { x + 16 }$ 
B)  $g ^ { - 1 } ( x ) = \sqrt { x + 16 }$ 
C)  $g ^ { - 1 } ( x ) = 4 + \sqrt { x }$ 
D)  $g ^ { - 1 } ( x ) = 4 - \sqrt { x }$ 
E)  none of these 
A)  $g ^ { - 1 } ( x ) = - \sqrt { x + 16 }$ 
B)  $g ^ { - 1 } ( x ) = \sqrt { x + 16 }$ 
C)  $g ^ { - 1 } ( x ) = 4 + \sqrt { x }$ 
D)  $g ^ { - 1 } ( x ) = 4 - \sqrt { x }$ 
E)  none of these

Question 15

Use a graphing calculator or computer to determine whether or not the function $f ( x ) = 2 x ^ { 3 } - x$  is one-to-one.

Accepted Answer

Using a graphing cal

Question 16

Determine whether $f ( x ) = x ^ { 2 } - x ^ { 6 }$ is even, odd, or neither.

Accepted Answer

A) even 
B) odd 
C) neither even nor odd 
D) both even and odd 
A) even 
B) odd 
C) neither even nor odd 
D) both even and odd

Question 17

Find the domain of the function. $$f ( x ) = \frac { 1 } { x } + \frac { 1 } { x + 1 }$$

Accepted Answer

A)  $( - \infty , 0 )$ 
B)  $( - \infty , - 1 ) \cup ( - 1,0 ) \cup ( 0 , \infty )$ 
C)  $( - \infty , - 1 ) \cup ( - 1,0 )$ 
D)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
E)  none of these 
A)  $( - \infty , 0 )$ 
B)  $( - \infty , - 1 ) \cup ( - 1,0 ) \cup ( 0 , \infty )$ 
C)  $( - \infty , - 1 ) \cup ( - 1,0 )$ 
D)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
E)  none of these

Question 18

Suppose the graph of f is given. Describe how the graph of the function $y = f ( x - 3 ) - 3$ 
can be obtained from the graph of 
f.

Accepted Answer

Shift the graph of f

Question 19

Determine which functions are one-to-one.

Accepted Answer

A)  I only 
B)  I, II 
C)  I, II, III 
D)  II only 
E)  III only 
A)  I only 
B)  I, II 
C)  I, II, III 
D)  II only 
E)  III only

Question 20

Determine whether the function in the figure is even, odd, or neither.

Accepted Answer

A)  even 
B)  odd 
C)  neither even or odd 
D)  both even and odd 
E)  not enough information to determine 
A)  even 
B)  odd 
C)  neither even or odd 
D)  both even and odd 
E)  not enough information to determine

Find the average rate of change of the function between the given points $f ( x ) = 2 x ^ { 2 } + x ; \quad x = 0 , x = 2$

Evaluate $f ( - 1 )$ , $f ( 0 )$ , $f ( 1 )$ , for the piecewise-defined function. $f ( x ) = \left\{ \begin{array} { l l } x ^ { 2 } & \text { if } x < 0 \\ x - 1 & \text { if } x \geq 0 \end{array} \right.$

Use a graphing calculator to determine approximately the internals on which the function $f$ is decreasing. $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + x ^ { 2 } - 24 x + 16$

Use a graphing calculator to determine approximately the internals on which the function $f$ is decreasing. $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + x ^ { 2 } - 24 x + 16$

Determine if the equation $x ^ { 2 } + ( y - 1 ) ^ { 2 } = 36$ defines y as a function of x

Find the domain of the function. $f ( x ) = 0.5 x - \frac { 2 } { \sqrt { x + 1 } }$

Determine whether or not the function $f ( x ) = - 2 x ^ { 2 } + 18 x - 16$ is one-to-one.

Sketch the graph of the piecewise defined function. $f ( x ) = \left\{ \begin{array} { l l } x + 2 & \text { if } x < 0 \\2 & \text { if } 0 \leq x \leq 1 \\3 - x & \text { if } 1 < x\end{array} \right.$

Use a graphing device to draw the graph of the function $f ( x ) = - 3 - 3 x ^ { 2 }$ . State approximately the interval(s) on which the function is increasing and on which the function is decreasing

Find the inverse of the function. $f ( x ) = 3 x + 2$

Find the inverse of the function. $g ( x ) = x ^ { 2 } - 9 , x \geq 0$

Find the inverse of the function. $g ( x ) = x ^ { 2 } - 16 , x \geq 0$

Use a graphing calculator or computer to determine whether or not the function $f ( x ) = 2 x ^ { 3 } - x$ is one-to-one.

Determine whether $f ( x ) = x ^ { 2 } - x ^ { 6 }$ is even, odd, or neither.

Find the domain of the function. $f ( x ) = \frac { 1 } { x } + \frac { 1 } { x + 1 }$

Suppose the graph of f is given. Describe how the graph of the function $y = f ( x - 3 ) - 3$ can be obtained from the graph of f.

Determine which functions are one-to-one.

Determine whether the function in the figure is even, odd, or neither.

Equations and Graphs

Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Right Triangle Approach

Trigonometric Functions: Unit Circle Approach

Conic Sections

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences and Series

Counting and Probability

Filters

Exam 3: Polynomial and Rational Functions

Find the average rate of change of the function between the given points f(x)=2x2+x;x=0,x=2f ( x ) = 2 x ^ { 2 } + x ; \quad x = 0 , x = 2f(x)=2x2+x;x=0,x=2

Evaluate f(−1)f ( - 1 )f(−1) , f(0)f ( 0 )f(0) , f(1)f ( 1 )f(1) , for the piecewise-defined function. f(x)={x2 if x<0x−1 if x≥0f ( x ) = \left\{ \begin{array} { l l } x ^ { 2 } & \text { if } x < 0 \\ x - 1 & \text { if } x \geq 0 \end{array} \right.f(x)={x2x−1​ if x<0 if x≥0​

Use a graphing calculator to determine approximately the internals on which the function fff is decreasing. f(x)=x4+6x3+x2−24x+16f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + x ^ { 2 } - 24 x + 16f(x)=x4+6x3+x2−24x+16

Use a graphing calculator to determine approximately the internals on which the function fff is decreasing. f(x)=x4+6x3+x2−24x+16f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + x ^ { 2 } - 24 x + 16f(x)=x4+6x3+x2−24x+16

Determine if the equation x2+(y−1)2=36x ^ { 2 } + ( y - 1 ) ^ { 2 } = 36x2+(y−1)2=36 defines y as a function of x

Find the domain of the function. f(x)=0.5x−2x+1f ( x ) = 0.5 x - \frac { 2 } { \sqrt { x + 1 } }f(x)=0.5x−x+1​2​

Determine whether or not the function f(x)=−2x2+18x−16f ( x ) = - 2 x ^ { 2 } + 18 x - 16f(x)=−2x2+18x−16 is one-to-one.

Use a graphing device to draw the graph of the function f(x)=−3−3x2f ( x ) = - 3 - 3 x ^ { 2 }f(x)=−3−3x2 . State approximately the interval(s) on which the function is increasing and on which the function is decreasing

Find the inverse of the function. f(x)=3x+2f ( x ) = 3 x + 2f(x)=3x+2

Find the inverse of the function. g(x)=x2−9,x≥0g ( x ) = x ^ { 2 } - 9 , x \geq 0g(x)=x2−9,x≥0

Find the inverse of the function. g(x)=x2−16,x≥0g ( x ) = x ^ { 2 } - 16 , x \geq 0g(x)=x2−16,x≥0

Use a graphing calculator or computer to determine whether or not the function f(x)=2x3−xf ( x ) = 2 x ^ { 3 } - xf(x)=2x3−x is one-to-one.

Determine whether f(x)=x2−x6f ( x ) = x ^ { 2 } - x ^ { 6 }f(x)=x2−x6 is even, odd, or neither.

Find the domain of the function. f(x)=1x+1x+1f ( x ) = \frac { 1 } { x } + \frac { 1 } { x + 1 }f(x)=x1​+x+11​

Suppose the graph of f is given. Describe how the graph of the function y=f(x−3)−3y = f ( x - 3 ) - 3y=f(x−3)−3 can be obtained from the graph of f.

Determine which functions are one-to-one.

Determine whether the function in the figure is even, odd, or neither.

Equations and Graphs

Functions

Exponential and Logarithmic Functions

Trigonometric Functions: Right Triangle Approach

Trigonometric Functions: Unit Circle Approach

Conic Sections

Polar Coordinates and Parametric Equations

Vectors in Two and Three Dimensions

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections

Sequences and Series

Counting and Probability

Filters

Find the average rate of change of the function between the given points $f ( x ) = 2 x ^ { 2 } + x ; \quad x = 0 , x = 2$

Evaluate $f ( - 1 )$ , $f ( 0 )$ , $f ( 1 )$ , for the piecewise-defined function. $f ( x ) = \left\{ \begin{array} { l l } x ^ { 2 } & \text { if } x < 0 \\ x - 1 & \text { if } x \geq 0 \end{array} \right.$

Use a graphing calculator to determine approximately the internals on which the function $f$ is decreasing. $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + x ^ { 2 } - 24 x + 16$

Use a graphing calculator to determine approximately the internals on which the function $f$ is decreasing. $f ( x ) = x ^ { 4 } + 6 x ^ { 3 } + x ^ { 2 } - 24 x + 16$

Determine if the equation $x ^ { 2 } + ( y - 1 ) ^ { 2 } = 36$ defines y as a function of x

Find the domain of the function. $f ( x ) = 0.5 x - \frac { 2 } { \sqrt { x + 1 } }$

Determine whether or not the function $f ( x ) = - 2 x ^ { 2 } + 18 x - 16$ is one-to-one.

Use a graphing device to draw the graph of the function $f ( x ) = - 3 - 3 x ^ { 2 }$ . State approximately the interval(s) on which the function is increasing and on which the function is decreasing

Find the inverse of the function. $f ( x ) = 3 x + 2$

Find the inverse of the function. $g ( x ) = x ^ { 2 } - 9 , x \geq 0$

Find the inverse of the function. $g ( x ) = x ^ { 2 } - 16 , x \geq 0$

Use a graphing calculator or computer to determine whether or not the function $f ( x ) = 2 x ^ { 3 } - x$ is one-to-one.

Determine whether $f ( x ) = x ^ { 2 } - x ^ { 6 }$ is even, odd, or neither.

Find the domain of the function. $f ( x ) = \frac { 1 } { x } + \frac { 1 } { x + 1 }$

Suppose the graph of f is given. Describe how the graph of the function $y = f ( x - 3 ) - 3$ can be obtained from the graph of f.