Question 1

Graph the function.
-$y=\sqrt{x-4}-3$

Accepted Answer

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

Question 2

Simplify the expression.
-$\ln \mathrm { e } ^ { 5 / 7 }$

Accepted Answer

A)  $\frac { 7 } { 5 } \mathrm { e }$ 
B)  $\frac { 5 } { 7 } \mathrm { e }$ 
C)  $\frac { 5 } { 7 }$ 
D)  $\frac { 7 } { 5 }$ 
A)  $\frac { 7 } { 5 } \mathrm { e }$ 
B)  $\frac { 5 } { 7 } \mathrm { e }$ 
C)  $\frac { 5 } { 7 }$ 
D)  $\frac { 7 } { 5 }$

Question 3

Solve the problem.
-A bacteria colony doubles in 5 hr. How long does it take the colony to triple? Use N $$\mathrm { N } = \mathrm { N } _ { 0 } 2 ^ { \mathrm { t } / \mathrm { T } }$$ , where N0 is the initial number of bacteria and T is the time in hours it takes the colony to double. (Round to the nearest
Hundredth, as necessary.)

Accepted Answer

A)  7.5 hr 
B)  15 hr 
C)  7.92 hr 
D)  2.03 hr 
A)  7.5 hr 
B)  15 hr 
C)  7.92 hr 
D)  2.03 hr

Question 4

Find the domain and range of the inverse of the given function.
-$$f ( x ) = - \frac { 1 } { x }$$

Accepted Answer

A)  Domain and range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  Domain: $( 0 , \infty )$; range: $( - \infty , 0 )$ 
C)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; range: $( - \infty , 0 )$ 
D)  Domain and range: all real numbers 
A)  Domain and range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  Domain: $( 0 , \infty )$; range: $( - \infty , 0 )$ 
C)  Domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; range: $( - \infty , 0 )$ 
D)  Domain and range: all real numbers

Question 5

Using the graph below, find the domain and range of the given function, and sketch the graph.  
-$y=-f(x)$

Accepted Answer

A)  D: $[ - 4,5 ] ; R : [ - 3,3 ]$
  
B)  D: $[ - 7.5,1 ] ; \mathrm { R } : [ - 1,5 ]$
  
C)  D: $[ - 5,4 ] ; R : [ - 3,3 ]$
  
D)  D: $[ - 7,2 ] ; R : [ - 4,2 ]$
  
A)  D: $[ - 4,5 ] ; R : [ - 3,3 ]$
  
B)  D: $[ - 7.5,1 ] ; \mathrm { R } : [ - 1,5 ]$
  
C)  D: $[ - 5,4 ] ; R : [ - 3,3 ]$
  
D)  D: $[ - 7,2 ] ; R : [ - 4,2 ]$

Question 6

Provide an appropriate response.
-Consider the graph of $\mathrm { f } ( \mathrm { x } ) = \sqrt { 9 - \mathrm { x } ^ { 2 } } , 0 \leq \mathrm { x } \leq 1$. What symmetry does the graph have? Is $\mathrm { f }$ its own inverse?

Accepted Answer

A)  The graph of $\mathrm { f }$ has no symmetry. The function $\mathrm { f }$ is not its own inverse because there is no symmetry. 
B)  The graph of $\mathrm { f }$ is symmetric with respect to the $\mathrm { y }$-axis. The function $\mathrm { f }$ is not its own inverse because $( f \circ f ) ( x ) = | x |$. 
C)  The graph of $\mathrm { f }$ is symmetric with respect to the $y$-axis. The function $\mathrm { f }$ is its own inverse because (f $\circ f ) ( x ) = x$. 
D)  The graph of $\mathrm { f }$ is symmetric with respect to the line $\mathrm { y } = \mathrm { x }$. The function $\mathrm { f }$ is its own inverse because (f of $) ( x ) = x$. 
A)  The graph of $\mathrm { f }$ has no symmetry. The function $\mathrm { f }$ is not its own inverse because there is no symmetry. 
B)  The graph of $\mathrm { f }$ is symmetric with respect to the $\mathrm { y }$-axis. The function $\mathrm { f }$ is not its own inverse because $( f \circ f ) ( x ) = | x |$. 
C)  The graph of $\mathrm { f }$ is symmetric with respect to the $y$-axis. The function $\mathrm { f }$ is its own inverse because (f $\circ f ) ( x ) = x$. 
D)  The graph of $\mathrm { f }$ is symmetric with respect to the line $\mathrm { y } = \mathrm { x }$. The function $\mathrm { f }$ is its own inverse because (f of $) ( x ) = x$.

Question 7

Determine an appropriate viewing window for the given function and use it to display its graph.
-$f ( x ) = - 0.7 x ^ { 6 } - x ^ { 5 } + 6 x ^ { 4 } - 5 x ^ { 3 } - 7 x ^ { 2 } + x - 3$

Accepted Answer

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

Question 8

Express the given quantity in terms of sin x or cos x.
-$\sin ( 4 \pi - x )$

Accepted Answer

A)  $\cos x - \sin x$ 
B)  $\sin x$ 
C)  $\sin ( - x )$ 
D)  $- \sin x$ 
A)  $\cos x - \sin x$ 
B)  $\sin x$ 
C)  $\sin ( - x )$ 
D)  $- \sin x$

Question 9

Graph the function.
-$y=(-3 x)^{2 / 3}-3$

Accepted Answer

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

Question 10

Determine if the function is even, odd, or neither.
-$$f ( x ) = \frac { - 6 } { x + 4 }$$

Accepted Answer

A)  Even 
B)  Odd 
C)  Neither 
A)  Even 
B)  Odd 
C)  Neither

Question 11

Express the given function as a composite of functions f and g such that y $$y = f ( g ( x ) )$$
-$$y = \frac { 8 } { \sqrt { 5 x + 1 } }$$

Accepted Answer

A)  $f ( x ) = \frac { 8 } { x } , g ( x ) = 5 x + 1$ 
B)  $f ( x ) = \sqrt { 5 x + 1 } , g ( x ) = 8$ 
C)  $f ( x ) = \frac { 8 } { \sqrt { x } } , g ( x ) = 5 x + 1$ 
D)  $f ( x ) = 8 , g ( x ) = \sqrt { 5 + 1 }$ 
A)  $f ( x ) = \frac { 8 } { x } , g ( x ) = 5 x + 1$ 
B)  $f ( x ) = \sqrt { 5 x + 1 } , g ( x ) = 8$ 
C)  $f ( x ) = \frac { 8 } { \sqrt { x } } , g ( x ) = 5 x + 1$ 
D)  $f ( x ) = 8 , g ( x ) = \sqrt { 5 + 1 }$

Question 12

Find the formula for the function.
-Express the perimeter of an isosceles triangle with side lengths x, 5x, and 5x as a function of the side length.

Accepted Answer

A)  p = 10x 
B)  $p=10 x^{3}$ 
C)  $p=25 x^{3}$ 
D)  p = 11x 
A)  p = 10x 
B)  $p=10 x^{3}$ 
C)  $p=25 x^{3}$ 
D)  p = 11x

Question 13

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval.
-$\tan x = \frac { 5 } { 12 } , \quad x$ in $\left[ \pi , \frac { 3 \pi } { 2 } \right]$

Accepted Answer

A)  $\sin x = \frac { 12 } { 13 } , \cos x = \frac { 5 } { 13 }$ 
B)  $\sin x = - \frac { 5 } { 13 } , \cos x = - \frac { 12 } { 13 }$ 
C)  $\sin x = \frac { 5 } { 13 } , \cos x = \frac { 12 } { 13 }$ 
D)  $\sin x = - \frac { 12 } { 13 } , \cos x = - \frac { 5 } { 13 }$ 
A)  $\sin x = \frac { 12 } { 13 } , \cos x = \frac { 5 } { 13 }$ 
B)  $\sin x = - \frac { 5 } { 13 } , \cos x = - \frac { 12 } { 13 }$ 
C)  $\sin x = \frac { 5 } { 13 } , \cos x = \frac { 12 } { 13 }$ 
D)  $\sin x = - \frac { 12 } { 13 } , \cos x = - \frac { 5 } { 13 }$

Question 14

Graph the function. Determine the symmetry, if any, of the function.
-$y = \frac { 1 } { x }$

Accepted Answer

A)  No symmetry
  
B)  Symmetric about the origin
  
C)  Symmetric about the origin
  
D)  Symmetric about the origin
  
A)  No symmetry
  
B)  Symmetric about the origin
  
C)  Symmetric about the origin
  
D)  Symmetric about the origin

Question 15

Is the function graphed below one-to-one?
-

Accepted Answer

A) True 
 B)False

Question 16

Express as a single logarithm and, if possible, simplify.
-$$\ln \left( 3 x ^ { 2 } - 9 x \right) + \ln \left( \frac { 1 } { 3 x } \right)$$

Accepted Answer

A)  $\ln \left( 3 x ^ { 2 } - 9 x + \frac { 1 } { 3 x } \right)$ 
B)  $\ln ( x - 3 )$ 
C)  $\ln ( x - 9 )$ 
D)  $\ln \left( 9 x ^ { 2 } ( x - 3 ) \right)$ 
A)  $\ln \left( 3 x ^ { 2 } - 9 x + \frac { 1 } { 3 x } \right)$ 
B)  $\ln ( x - 3 )$ 
C)  $\ln ( x - 9 )$ 
D)  $\ln \left( 9 x ^ { 2 } ( x - 3 ) \right)$

Question 17

Use a graphing calculator or computer to determine which of the given viewing windows displays the most appropriate
graph of the specified function.
-$f ( x ) = x ^ { 4 } - 7 x ^ { 2 } + 3 x$

Accepted Answer

A)  $[ - 5,5 ]$ by $[ - 10,15 ]$ 
B)  $[ - 5,5 ]$ by $[ - 25,15 ]$ 
C)  $[ - 10,15 ]$ by $[ - 5,5 ]$ 
D)  $[ - 25,15 ]$ by $[ - 5,5 ]$ 
A)  $[ - 5,5 ]$ by $[ - 10,15 ]$ 
B)  $[ - 5,5 ]$ by $[ - 25,15 ]$ 
C)  $[ - 10,15 ]$ by $[ - 5,5 ]$ 
D)  $[ - 25,15 ]$ by $[ - 5,5 ]$

Question 18

Express the given function as a composite of functions f and g such that y $$y = f ( g ( x ) )$$
-$$y = \frac { 6 } { x ^ { 2 } } + 5$$

Accepted Answer

A)  $f ( x ) = x , g ( x ) = \frac { 6 } { x } + 5$ 
B)  $f ( x ) = \frac { 1 } { x } , g ( x ) = \frac { 6 } { x } + 5$ 
C)  $f ( x ) = \frac { 6 } { x ^ { 2 } } , g ( x ) = 5$ 
D)  $f ( x ) = x + 5 , g ( x ) = \frac { 6 } { x ^ { 2 } }$ 
A)  $f ( x ) = x , g ( x ) = \frac { 6 } { x } + 5$ 
B)  $f ( x ) = \frac { 1 } { x } , g ( x ) = \frac { 6 } { x } + 5$ 
C)  $f ( x ) = \frac { 6 } { x ^ { 2 } } , g ( x ) = 5$ 
D)  $f ( x ) = x + 5 , g ( x ) = \frac { 6 } { x ^ { 2 } }$

Question 19

Is the function graphed below one-to-one?
-

Accepted Answer

A) True 
 B)False

Question 20

Express the given quantity in terms of sin x or cos x.
-$\cos ( 3 \pi + x )$

Accepted Answer

A)  $- \sin x$ 
B)  $- \cos x$ 
C)  $\cos x$ 
D)  $\sin x - \cos x$ 
A)  $- \sin x$ 
B)  $- \cos x$ 
C)  $\cos x$ 
D)  $\sin x - \cos x$

Graph the function. - $y=\sqrt{x-4}-3$ $Graph the function. - y=\sqrt{x-4}-3$

Simplify the expression. - $\ln \mathrm { e } ^ { 5 / 7 }$

Find the domain and range of the inverse of the given function. - $f ( x ) = - \frac { 1 } { x }$

Using the graph below, find the domain and range of the given function, and sketch the graph. - $y=-f(x)$

Provide an appropriate response. -Consider the graph of $\mathrm { f } ( \mathrm { x } ) = \sqrt { 9 - \mathrm { x } ^ { 2 } } , 0 \leq \mathrm { x } \leq 1$ . What symmetry does the graph have? Is $\mathrm { f }$ its own inverse?

Express the given quantity in terms of sin x or cos x. - $\sin ( 4 \pi - x )$

Graph the function. - $y=(-3 x)^{2 / 3}-3$ $Graph the function. - y=(-3 x)^{2 / 3}-3$

Determine if the function is even, odd, or neither. - $f ( x ) = \frac { - 6 } { x + 4 }$

Express the given function as a composite of functions f and g such that y $y = f ( g ( x ) )$ - $y = \frac { 8 } { \sqrt { 5 x + 1 } }$

Find the formula for the function. -Express the perimeter of an isosceles triangle with side lengths x, 5x, and 5x as a function of the side length.

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval. - $\tan x = \frac { 5 } { 12 } , \quad x$ in $\left[ \pi , \frac { 3 \pi } { 2 } \right]$

Graph the function. Determine the symmetry, if any, of the function. - $y = \frac { 1 } { x }$ $Graph the function. Determine the symmetry, if any, of the function. - y = \frac { 1 } { x }$

Is the function graphed below one-to-one? -

Express as a single logarithm and, if possible, simplify. - $\ln \left( 3 x ^ { 2 } - 9 x \right) + \ln \left( \frac { 1 } { 3 x } \right)$

Use a graphing calculator or computer to determine which of the given viewing windows displays the most appropriate graph of the specified function. - $f ( x ) = x ^ { 4 } - 7 x ^ { 2 } + 3 x$

Express the given function as a composite of functions f and g such that y $y = f ( g ( x ) )$ - $y = \frac { 6 } { x ^ { 2 } } + 5$

Is the function graphed below one-to-one? -

Express the given quantity in terms of sin x or cos x. - $\cos ( 3 \pi + x )$

Limits and Continuity

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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

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Vector-Valued Functions and Motion in Space

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Multiple Integrals

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Exam 2: Functions

Graph the function. - y=x−4−3y=\sqrt{x-4}-3y=x−4​−3

Simplify the expression. - ln⁡e5/7\ln \mathrm { e } ^ { 5 / 7 }lne5/7

Find the domain and range of the inverse of the given function. - f(x)=−1xf ( x ) = - \frac { 1 } { x }f(x)=−x1​

Using the graph below, find the domain and range of the given function, and sketch the graph. - y=−f(x)y=-f(x)y=−f(x)

Provide an appropriate response. -Consider the graph of f(x)=9−x2,0≤x≤1\mathrm { f } ( \mathrm { x } ) = \sqrt { 9 - \mathrm { x } ^ { 2 } } , 0 \leq \mathrm { x } \leq 1f(x)=9−x2​,0≤x≤1 . What symmetry does the graph have? Is f\mathrm { f }f its own inverse?

Determine an appropriate viewing window for the given function and use it to display its graph. - f(x)=−0.7x6−x5+6x4−5x3−7x2+x−3f ( x ) = - 0.7 x ^ { 6 } - x ^ { 5 } + 6 x ^ { 4 } - 5 x ^ { 3 } - 7 x ^ { 2 } + x - 3f(x)=−0.7x6−x5+6x4−5x3−7x2+x−3

Express the given quantity in terms of sin x or cos x. - sin⁡(4π−x)\sin ( 4 \pi - x )sin(4π−x)

Graph the function. - y=(−3x)2/3−3y=(-3 x)^{2 / 3}-3y=(−3x)2/3−3

Determine if the function is even, odd, or neither. - f(x)=−6x+4f ( x ) = \frac { - 6 } { x + 4 }f(x)=x+4−6​

Express the given function as a composite of functions f and g such that y y=f(g(x))y = f ( g ( x ) )y=f(g(x)) - y=85x+1y = \frac { 8 } { \sqrt { 5 x + 1 } }y=5x+1​8​

Find the formula for the function. -Express the perimeter of an isosceles triangle with side lengths x, 5x, and 5x as a function of the side length.

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval. - tan⁡x=512,x\tan x = \frac { 5 } { 12 } , \quad xtanx=125​,x in [π,3π2]\left[ \pi , \frac { 3 \pi } { 2 } \right][π,23π​]

Graph the function. Determine the symmetry, if any, of the function. - y=1xy = \frac { 1 } { x }y=x1​

Is the function graphed below one-to-one? -

Express as a single logarithm and, if possible, simplify. - ln⁡(3x2−9x)+ln⁡(13x)\ln \left( 3 x ^ { 2 } - 9 x \right) + \ln \left( \frac { 1 } { 3 x } \right)ln(3x2−9x)+ln(3x1​)

Use a graphing calculator or computer to determine which of the given viewing windows displays the most appropriate graph of the specified function. - f(x)=x4−7x2+3xf ( x ) = x ^ { 4 } - 7 x ^ { 2 } + 3 xf(x)=x4−7x2+3x

Express the given function as a composite of functions f and g such that y y=f(g(x))y = f ( g ( x ) )y=f(g(x)) - y=6x2+5y = \frac { 6 } { x ^ { 2 } } + 5y=x26​+5

Is the function graphed below one-to-one? -

Express the given quantity in terms of sin x or cos x. - cos⁡(3π+x)\cos ( 3 \pi + x )cos(3π+x)

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

Graph the function. - $y=\sqrt{x-4}-3$ $Graph the function. - y=\sqrt{x-4}-3$

Simplify the expression. - $\ln \mathrm { e } ^ { 5 / 7 }$

Find the domain and range of the inverse of the given function. - $f ( x ) = - \frac { 1 } { x }$

Using the graph below, find the domain and range of the given function, and sketch the graph. - $y=-f(x)$

Provide an appropriate response. -Consider the graph of $\mathrm { f } ( \mathrm { x } ) = \sqrt { 9 - \mathrm { x } ^ { 2 } } , 0 \leq \mathrm { x } \leq 1$ . What symmetry does the graph have? Is $\mathrm { f }$ its own inverse?

Express the given quantity in terms of sin x or cos x. - $\sin ( 4 \pi - x )$

Graph the function. - $y=(-3 x)^{2 / 3}-3$ $Graph the function. - y=(-3 x)^{2 / 3}-3$

Determine if the function is even, odd, or neither. - $f ( x ) = \frac { - 6 } { x + 4 }$

Express the given function as a composite of functions f and g such that y $y = f ( g ( x ) )$ - $y = \frac { 8 } { \sqrt { 5 x + 1 } }$

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval. - $\tan x = \frac { 5 } { 12 } , \quad x$ in $\left[ \pi , \frac { 3 \pi } { 2 } \right]$

Graph the function. Determine the symmetry, if any, of the function. - $y = \frac { 1 } { x }$ $Graph the function. Determine the symmetry, if any, of the function. - y = \frac { 1 } { x }$

Express as a single logarithm and, if possible, simplify. - $\ln \left( 3 x ^ { 2 } - 9 x \right) + \ln \left( \frac { 1 } { 3 x } \right)$

Use a graphing calculator or computer to determine which of the given viewing windows displays the most appropriate graph of the specified function. - $f ( x ) = x ^ { 4 } - 7 x ^ { 2 } + 3 x$

Express the given function as a composite of functions f and g such that y $y = f ( g ( x ) )$ - $y = \frac { 6 } { x ^ { 2 } } + 5$

Express the given quantity in terms of sin x or cos x. - $\cos ( 3 \pi + x )$