Question 1

Find the domain and graph the function.
-$g(x)=-9-3 x-x^{2}$

Accepted Answer

A)  D: $\left( - \infty , - \frac { 27 } { 4 } \right]$
  
B)  D: $( - \infty , \infty )$
  
C)  D: $( - \infty , \infty )$
  
D)  D: $( - \infty , \infty )$
  
A)  D: $\left( - \infty , - \frac { 27 } { 4 } \right]$
  
B)  D: $( - \infty , \infty )$
  
C)  D: $( - \infty , \infty )$
  
D)  D: $( - \infty , \infty )$

Question 2

Determine an appropriate viewing window for the given function and use it to display its graph.
-$f ( x ) = x ^ { 5 } - x ^ { 3 } + x ^ { 2 } + 4$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 3

Determine an appropriate viewing window for the given function and use it to display its graph.
-$f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } - 4 }$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 4

State the domain and range of the function.
-$$f ( x ) = - 6 e ^ { - x } + 1$$

Accepted Answer

A)  domain: $( - \infty , \infty ) \cup ( - \infty , \infty )$; range: $( - \infty , 1 )$ 
B)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $( - \infty , 1 ]$ 
D)  domain: $( - \infty , \infty )$; range: $( - \infty , 1 )$ 
A)  domain: $( - \infty , \infty ) \cup ( - \infty , \infty )$; range: $( - \infty , 1 )$ 
B)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $( - \infty , 1 ]$ 
D)  domain: $( - \infty , \infty )$; range: $( - \infty , 1 )$

Question 5

Solve the problem.
-If $f ( x ) = 3 x + 8$ and $g ( x ) = 2 x - 1$, find $f ( g ( x ) )$.

Accepted Answer

A)  $6 x + 11$ 
B)  $6 x + 5$ 
C)  $6 x + 7$ 
D)  $6 x + 15$ 
A)  $6 x + 11$ 
B)  $6 x + 5$ 
C)  $6 x + 7$ 
D)  $6 x + 15$

Question 6

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) 
  
A) 
  
B) 
  
C) 
  
D)

Question 7

Graph the function. Determine the symmetry, if any, of the function.
-$y=2 \sqrt{x}$

Accepted Answer

A)  No symmetry
  
B)  Symmetric about the x-axis
  
C)  No symmetry
  
D)  Symmetric about the $x$-axis
  
A)  No symmetry
  
B)  Symmetric about the x-axis
  
C)  No symmetry
  
D)  Symmetric about the $x$-axis

Question 8

Graph the function. Determine the symmetry, if any, of the function.
-$y=(-x)^{5 / 2}$

Accepted Answer

A)  No symmetry
  
B)  Symmetric about the $y$-axis
  
C)  No symmetry
  
D)  Symmetric about the $y$-axis
  
A)  No symmetry
  
B)  Symmetric about the $y$-axis
  
C)  No symmetry
  
D)  Symmetric about the $y$-axis

Question 9

Find the inverse of the function.
-$$f ( x ) = ( x - 5 ) ^ { 2 } , x \geq 5$$

Accepted Answer

A)  Not a one-to-one function 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } - 5 } , \mathrm { x } \geq 5$ 
C)  $f ^ { - 1 } ( x ) = \sqrt { x } + 5 , x \geq 0$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - \sqrt { \mathrm { x } } + 5 , \mathrm { x } \geq 0$ 
A)  Not a one-to-one function 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = \sqrt { \mathrm { x } - 5 } , \mathrm { x } \geq 5$ 
C)  $f ^ { - 1 } ( x ) = \sqrt { x } + 5 , x \geq 0$ 
D)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = - \sqrt { \mathrm { x } } + 5 , \mathrm { x } \geq 0$

Question 10

Graph the function.
-$\text { Graph the lower branch of the hyperbola } y ^ { 2 } - 4 x ^ { 2 } = 1 \text {. }$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 11

Simplify the expression.
-$\mathrm { e } ^ { \ln x + \ln y }$

Accepted Answer

A)  $x + y$ 
B)  $e ^ { x } e ^ { y }$ 
C)  $\ln x + \ln y$ 
D)  $x y$ 
A)  $x + y$ 
B)  $e ^ { x } e ^ { y }$ 
C)  $\ln x + \ln y$ 
D)  $x y$

Question 12

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval.
-$\sin x = - \frac { \sqrt { 3 } } { 2 } , \quad x$ in $\left[ - \frac { \pi } { 2 } , 0 \right]$

Accepted Answer

A)  $\cos x = \frac { 1 } { 2 } , \tan x = - \sqrt { 3 }$ 
B)  $\cos x = - 2 , \tan x = \frac { \sqrt { 3 } } { 3 }$ 
C)  $\cos x = \frac { 1 } { 2 } , \tan x = \sqrt { 3 }$ 
D)  $\cos x = - \frac { 1 } { 2 } , \tan x = - \sqrt { 3 }$ 
A)  $\cos x = \frac { 1 } { 2 } , \tan x = - \sqrt { 3 }$ 
B)  $\cos x = - 2 , \tan x = \frac { \sqrt { 3 } } { 3 }$ 
C)  $\cos x = \frac { 1 } { 2 } , \tan x = \sqrt { 3 }$ 
D)  $\cos x = - \frac { 1 } { 2 } , \tan x = - \sqrt { 3 }$

Question 13

Use the laws of exponents to simplify. Do not use negative exponents in your answer.
-$$\frac { 9 ^ { 8 / 13 } } { 9 ^ { - 3 / 13 } }$$

Accepted Answer

A)  $9 ^ { 8 / 13 } - 9 ^ { 3 / 13 }$ 
B)  $95 / 13$ 
C)  $9 ^ { 11 / 13 }$ 
D)  $9 ^ { - 24 / 169 }$ 
A)  $9 ^ { 8 / 13 } - 9 ^ { 3 / 13 }$ 
B)  $95 / 13$ 
C)  $9 ^ { 11 / 13 }$ 
D)  $9 ^ { - 24 / 169 }$

Question 14

Determine from its graph if the function is one-to-one.
-$$f ( x ) = \left\{ \begin{array} { l l } 
1 + \frac { x } { 5 } , & x \geq 0 \
\frac { x } { x - 5 } , & x < 0
\end{array} \right.$$

Accepted Answer

A) True 
 B)False

Question 15

Assume that f is an even function, g is an odd function, and both f and g are defined on the entire real line. State whether
the combination of functions (where defined) is even or odd.
-$$f \circ g$$

Accepted Answer

A)  Even 
B)  Odd 
A)  Even 
B)  Odd

Question 16

Rewrite the ratio as a ratio of natural logarithms and simplify.
-$\frac { \log _ { 243 } x } { \log 3 x }$

Accepted Answer

A)  $\frac { 1 } { 5 }$ 
B)  $3 ^ { 4 }$ 
C)  $\ln 5$ 
D)  $\frac { 1 } { 3 ^ { 4 } }$ 
A)  $\frac { 1 } { 5 }$ 
B)  $3 ^ { 4 }$ 
C)  $\ln 5$ 
D)  $\frac { 1 } { 3 ^ { 4 } }$

Question 17

Solve the problem.
-The table shows the average weight for women of medium frame based on height. Find a regression line for the data.
$\begin{array}{cc}
\hline \text { Height (in.) } & \text { Weight (lb) } \
\hline 60 & 118 \
61 & 120 \
62 & 125.5 \
63 & 129 \
64 & 133 \
65 & 136.5 \
66 & 138 \
67 & 142 \
68 & 144 \
69 & 147 \
\hline
\end{array}$

Accepted Answer

A)  $y = 3.9941 x - 68.5636$ 
B)  $y = 3.8428 x - 73.7191$ 
C)  $y = 4.5781 x - 52.6742$ 
D)  $y = 3.2848 x - 78.5727$ 
A)  $y = 3.9941 x - 68.5636$ 
B)  $y = 3.8428 x - 73.7191$ 
C)  $y = 4.5781 x - 52.6742$ 
D)  $y = 3.2848 x - 78.5727$

Question 18

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth.
-$$6 ^ { 3 x } = 8 ^ { x + 1 }$$

Accepted Answer

A)  -7.228 
B)  1.161 
C)  0.631 
D)  2.161 
A)  -7.228 
B)  1.161 
C)  0.631 
D)  2.161

Question 19

Graph the function.
-$$y = \frac { 1 } { x ^ { 2 } } - 4$$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Question 20

Match the equation with its graph.
-$y = x ^ { 3 }$

Accepted Answer

A) 
  
B) 
  
C) 
  
D) 
  
A) 
  
B) 
  
C) 
  
D)

Find the domain and graph the function. - $g(x)=-9-3 x-x^{2}$ $Find the domain and graph the function. - g(x)=-9-3 x-x^{2}$

Determine an appropriate viewing window for the given function and use it to display its graph. - $f ( x ) = x ^ { 5 } - x ^ { 3 } + x ^ { 2 } + 4$ $Determine an appropriate viewing window for the given function and use it to display its graph. - f ( x ) = x ^ { 5 } - x ^ { 3 } + x ^ { 2 } + 4$

Determine an appropriate viewing window for the given function and use it to display its graph. - $f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } - 4 }$ $Determine an appropriate viewing window for the given function and use it to display its graph. - f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } - 4 }$

State the domain and range of the function. - $f ( x ) = - 6 e ^ { - x } + 1$

Solve the problem. -If $f ( x ) = 3 x + 8$ and $g ( x ) = 2 x - 1$ , find $f ( g ( x ) )$ .

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

Graph the function. Determine the symmetry, if any, of the function. - $y=2 \sqrt{x}$ $Graph the function. Determine the symmetry, if any, of the function. - y=2 \sqrt{x}$

Graph the function. Determine the symmetry, if any, of the function. - $y=(-x)^{5 / 2}$ $Graph the function. Determine the symmetry, if any, of the function. - y=(-x)^{5 / 2}$

Find the inverse of the function. - $f ( x ) = ( x - 5 ) ^ { 2 } , x \geq 5$

Graph the function. - $\text { Graph the lower branch of the hyperbola } y ^ { 2 } - 4 x ^ { 2 } = 1 \text {. }$ $Graph the function. - \text { Graph the lower branch of the hyperbola } y ^ { 2 } - 4 x ^ { 2 } = 1 \text {. }$

Simplify the expression. - $\mathrm { e } ^ { \ln x + \ln y }$

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval. - $\sin x = - \frac { \sqrt { 3 } } { 2 } , \quad x$ in $\left[ - \frac { \pi } { 2 } , 0 \right]$

Use the laws of exponents to simplify. Do not use negative exponents in your answer. - $\frac { 9 ^ { 8 / 13 } } { 9 ^ { - 3 / 13 } }$

Determine from its graph if the function is one-to-one. - $f ( x ) = \left\{ \begin{array} { l l } 1 + \frac { x } { 5 } , & x \geq 0 \\\frac { x } { x - 5 } , & x < 0\end{array} \right.$

Assume that f is an even function, g is an odd function, and both f and g are defined on the entire real line. State whether the combination of functions (where defined) is even or odd. - $f \circ g$

Rewrite the ratio as a ratio of natural logarithms and simplify. - $\frac { \log _ { 243 } x } { \log 3 x }$

Solve the problem. -The table shows the average weight for women of medium frame based on height. Find a regression line for the data. Height (in.) Weight (lb) 60 118 61 120 62 125.5 63 129 64 133 65 136.5 66 138 67 142 68 144 69 147

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - $6 ^ { 3 x } = 8 ^ { x + 1 }$

Graph the function. - $y = \frac { 1 } { x ^ { 2 } } - 4$ $Graph the function. - y = \frac { 1 } { x ^ { 2 } } - 4$

Match the equation with its graph. - $y = x ^ { 3 }$

Limits and Continuity

Derivatives

Applications of Derivatives

Integrals

Applications of Definite Integrals

Integrals and Transcendental Functions

Techniques of Integration

First-Order Differential Equations

Infinite Sequences and Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions and Motion in Space

Partial Derivatives

Multiple Integrals

Integrals and Vector Fields

Filters

Exam 2: Functions

Find the domain and graph the function. - g(x)=−9−3x−x2g(x)=-9-3 x-x^{2}g(x)=−9−3x−x2

Determine an appropriate viewing window for the given function and use it to display its graph. - f(x)=x5−x3+x2+4f ( x ) = x ^ { 5 } - x ^ { 3 } + x ^ { 2 } + 4f(x)=x5−x3+x2+4

Determine an appropriate viewing window for the given function and use it to display its graph. - f(x)=x3x2−4f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } - 4 }f(x)=x2−4x3​

State the domain and range of the function. - f(x)=−6e−x+1f ( x ) = - 6 e ^ { - x } + 1f(x)=−6e−x+1

Solve the problem. -If f(x)=3x+8f ( x ) = 3 x + 8f(x)=3x+8 and g(x)=2x−1g ( x ) = 2 x - 1g(x)=2x−1 , find f(g(x))f ( g ( x ) )f(g(x)) .

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

Graph the function. Determine the symmetry, if any, of the function. - y=2xy=2 \sqrt{x}y=2x​

Graph the function. Determine the symmetry, if any, of the function. - y=(−x)5/2y=(-x)^{5 / 2}y=(−x)5/2

Find the inverse of the function. - f(x)=(x−5)2,x≥5f ( x ) = ( x - 5 ) ^ { 2 } , x \geq 5f(x)=(x−5)2,x≥5

Graph the function. - Graph the lower branch of the hyperbola y2−4x2=1. \text { Graph the lower branch of the hyperbola } y ^ { 2 } - 4 x ^ { 2 } = 1 \text {. } Graph the lower branch of the hyperbola y2−4x2=1.

Simplify the expression. - eln⁡x+ln⁡y\mathrm { e } ^ { \ln x + \ln y }elnx+lny

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval. - sin⁡x=−32,x\sin x = - \frac { \sqrt { 3 } } { 2 } , \quad xsinx=−23​​,x in [−π2,0]\left[ - \frac { \pi } { 2 } , 0 \right][−2π​,0]

Use the laws of exponents to simplify. Do not use negative exponents in your answer. - 98/139−3/13\frac { 9 ^ { 8 / 13 } } { 9 ^ { - 3 / 13 } }9−3/1398/13​

Determine from its graph if the function is one-to-one. - f(x)={1+x5,x≥0xx−5,x<0f ( x ) = \left\{ \begin{array} { l l } 1 + \frac { x } { 5 } , & x \geq 0 \\\frac { x } { x - 5 } , & x < 0\end{array} \right.f(x)={1+5x​,x−5x​,​x≥0x<0​

Assume that f is an even function, g is an odd function, and both f and g are defined on the entire real line. State whether the combination of functions (where defined) is even or odd. - f∘gf \circ gf∘g

Rewrite the ratio as a ratio of natural logarithms and simplify. - log⁡243xlog⁡3x\frac { \log _ { 243 } x } { \log 3 x }log3xlog243​x​

Solve the problem. -The table shows the average weight for women of medium frame based on height. Find a regression line for the data. Height (in.) Weight (lb) 60 118 61 120 62 125.5 63 129 64 133 65 136.5 66 138 67 142 68 144 69 147

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - 63x=8x+16 ^ { 3 x } = 8 ^ { x + 1 }63x=8x+1

Graph the function. - y=1x2−4y = \frac { 1 } { x ^ { 2 } } - 4y=x21​−4

Match the equation with its graph. - y=x3y = x ^ { 3 }y=x3

Limits and Continuity

Derivatives

Applications of Derivatives

Integrals

Applications of Definite Integrals

Integrals and Transcendental Functions

Techniques of Integration

First-Order Differential Equations

Infinite Sequences and Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions and Motion in Space

Partial Derivatives

Multiple Integrals

Integrals and Vector Fields

Filters

Find the domain and graph the function. - $g(x)=-9-3 x-x^{2}$ $Find the domain and graph the function. - g(x)=-9-3 x-x^{2}$

Determine an appropriate viewing window for the given function and use it to display its graph. - $f ( x ) = x ^ { 5 } - x ^ { 3 } + x ^ { 2 } + 4$ $Determine an appropriate viewing window for the given function and use it to display its graph. - f ( x ) = x ^ { 5 } - x ^ { 3 } + x ^ { 2 } + 4$

Determine an appropriate viewing window for the given function and use it to display its graph. - $f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } - 4 }$ $Determine an appropriate viewing window for the given function and use it to display its graph. - f ( x ) = \frac { x ^ { 3 } } { x ^ { 2 } - 4 }$

State the domain and range of the function. - $f ( x ) = - 6 e ^ { - x } + 1$

Solve the problem. -If $f ( x ) = 3 x + 8$ and $g ( x ) = 2 x - 1$ , find $f ( g ( x ) )$ .

Graph the function. Determine the symmetry, if any, of the function. - $y=2 \sqrt{x}$ $Graph the function. Determine the symmetry, if any, of the function. - y=2 \sqrt{x}$

Graph the function. Determine the symmetry, if any, of the function. - $y=(-x)^{5 / 2}$ $Graph the function. Determine the symmetry, if any, of the function. - y=(-x)^{5 / 2}$

Find the inverse of the function. - $f ( x ) = ( x - 5 ) ^ { 2 } , x \geq 5$

Graph the function. - $\text { Graph the lower branch of the hyperbola } y ^ { 2 } - 4 x ^ { 2 } = 1 \text {. }$ $Graph the function. - \text { Graph the lower branch of the hyperbola } y ^ { 2 } - 4 x ^ { 2 } = 1 \text {. }$

Simplify the expression. - $\mathrm { e } ^ { \ln x + \ln y }$

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval. - $\sin x = - \frac { \sqrt { 3 } } { 2 } , \quad x$ in $\left[ - \frac { \pi } { 2 } , 0 \right]$

Use the laws of exponents to simplify. Do not use negative exponents in your answer. - $\frac { 9 ^ { 8 / 13 } } { 9 ^ { - 3 / 13 } }$

Determine from its graph if the function is one-to-one. - $f ( x ) = \left\{ \begin{array} { l l } 1 + \frac { x } { 5 } , & x \geq 0 \\\frac { x } { x - 5 } , & x < 0\end{array} \right.$

Assume that f is an even function, g is an odd function, and both f and g are defined on the entire real line. State whether the combination of functions (where defined) is even or odd. - $f \circ g$

Rewrite the ratio as a ratio of natural logarithms and simplify. - $\frac { \log _ { 243 } x } { \log 3 x }$

Use a graph to find an approximate solution to the equation. Round to the nearest thousandth. - $6 ^ { 3 x } = 8 ^ { x + 1 }$

Graph the function. - $y = \frac { 1 } { x ^ { 2 } } - 4$ $Graph the function. - y = \frac { 1 } { x ^ { 2 } } - 4$

Match the equation with its graph. - $y = x ^ { 3 }$