Question 1

Determine if the function is even, odd, or neither.
-$$h ( t ) = \sqrt { t ^ { 2 } - 6 }$$

Accepted Answer

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

Question 2

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

Accepted Answer

A) True 
 B)False

Question 3

Express the following logarithm as specified.
-$\frac { \ln 35 + \ln ( 1 / 7 ) } { \ln 625 }$ in terms of $\ln 5$ and $\ln 7$

Accepted Answer

A)  $\frac { \ln 7 } { 4 }$ 
B)  1 
C)  $\frac { \ln 5 } { 2 }$ 
D)  $\frac { 1 } { 4 }$ 
A)  $\frac { \ln 7 } { 4 }$ 
B)  1 
C)  $\frac { \ln 5 } { 2 }$ 
D)  $\frac { 1 } { 4 }$

Question 4

Rewrite the ratio as a ratio of natural logarithms and simplify.
-$\frac { \log _ { 10 } x } { \log _ { 11 } x }$

Accepted Answer

A)  $\frac { 11 } { 10 }$ 
B)  $\frac { 10 } { 11 }$ 
C)  $\frac { \ln 11 } { \ln 10 }$ 
D)  $\frac { \ln 10 } { \ln 11 }$ 
A)  $\frac { 11 } { 10 }$ 
B)  $\frac { 10 } { 11 }$ 
C)  $\frac { \ln 11 } { \ln 10 }$ 
D)  $\frac { \ln 10 } { \ln 11 }$

Question 5

State the domain and range of the function.
-$$f ( x ) = 2 ^ { - x } + 2$$

Accepted Answer

A)  domain: $( - \infty , \infty ) \cup ( - \infty , \infty )$; range: $( - \infty , 2 )$ 
B)  domain: $( - \infty , \infty )$; range: $( - \infty , 2 )$ 
C)  domain: $( - \infty , \infty )$; range: $( - \infty , 2 ]$ 
D)  domain: $( - \infty , \infty )$; range: $( 2 , \infty )$ 
A)  domain: $( - \infty , \infty ) \cup ( - \infty , \infty )$; range: $( - \infty , 2 )$ 
B)  domain: $( - \infty , \infty )$; range: $( - \infty , 2 )$ 
C)  domain: $( - \infty , \infty )$; range: $( - \infty , 2 ]$ 
D)  domain: $( - \infty , \infty )$; range: $( 2 , \infty )$

Question 6

Use the appropriate addition formula to find the exact value of the expression.
-$\tan \left( \frac { 13 \pi } { 12 } \right)$

Accepted Answer

A)  $\frac { 2 + \sqrt { 3 } } { 4 }$ 
B)  $2 + \sqrt { 3 }$ 
C)  $\frac { 2 - \sqrt { 3 } } { 4 }$ 
D)  $2 - \sqrt { 3 }$ 
A)  $\frac { 2 + \sqrt { 3 } } { 4 }$ 
B)  $2 + \sqrt { 3 }$ 
C)  $\frac { 2 - \sqrt { 3 } } { 4 }$ 
D)  $2 - \sqrt { 3 }$

Question 7

Find the exact value of the trigonometric function. Do not use a calculator or tables.
-$\tan \left( \frac { 4 \pi } { 3 } \right)$

Accepted Answer

A)  $\sqrt { 3 }$ 
B)  1 
C)  $- \sqrt { 3 }$ 
D)  $- \frac { \sqrt { 3 } } { 3 }$ 
A)  $\sqrt { 3 }$ 
B)  1 
C)  $- \sqrt { 3 }$ 
D)  $- \frac { \sqrt { 3 } } { 3 }$

Question 8

Provide an appropriate response.
-Find the inverse of the function $f ( x ) = x + 5$. How is the graph of $f ^ { - 1 }$ related to the graph of $f$ ?

Accepted Answer

A)  $f ( x ) = \frac { 1 } { x } + 5$. The graph of $f ^ { - 1 }$ is a curve intersecting the graph of $f$ at two points equidistant from the $y$-axis. 
B)  $f ( x ) = x + \frac { 1 } { 5 }$. The graph of $f ^ { - 1 }$ is a line parallel to the graph of $f$. The graphs of $f$ and $f ^ { - 1 }$ lie on the same side of the line $y = x$. 
C)  $f ( x ) = - x - 5$. The graph of $f ^ { - 1 }$ is a line perpendicular to the graph of $f$ at $x = 5$. 
D)  $f ( x ) = x - 5$. The graph of $f ^ { - 1 }$ is a line parallel to the graph of $f$. The graphs of $f$ and $f ^ { - 1 }$ lie on opposite sides of the line $y = x$ and are equidistant from that line. 
A)  $f ( x ) = \frac { 1 } { x } + 5$. The graph of $f ^ { - 1 }$ is a curve intersecting the graph of $f$ at two points equidistant from the $y$-axis. 
B)  $f ( x ) = x + \frac { 1 } { 5 }$. The graph of $f ^ { - 1 }$ is a line parallel to the graph of $f$. The graphs of $f$ and $f ^ { - 1 }$ lie on the same side of the line $y = x$. 
C)  $f ( x ) = - x - 5$. The graph of $f ^ { - 1 }$ is a line perpendicular to the graph of $f$ at $x = 5$. 
D)  $f ( x ) = x - 5$. The graph of $f ^ { - 1 }$ is a line parallel to the graph of $f$. The graphs of $f$ and $f ^ { - 1 }$ lie on opposite sides of the line $y = x$ and are equidistant from that line.

Question 9

Find the formula for the function.
-Express the length d of a square's diagonal as a function of its side length x.

Accepted Answer

A)  $d=x \sqrt{2}$ 
B)  d = 2x 
C) $d=x \sqrt{3}$ 
D)  d = x 
A)  $d=x \sqrt{2}$ 
B)  d = 2x 
C) $d=x \sqrt{3}$ 
D)  d = x

Question 10

Graph the function.
-$y-4=x^{2 / 3}$

Accepted Answer

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

Question 11

Express the given function as a composite of functions f and g such that y $$y = f ( g ( x ) )$$
-$$y = | 7 x + 4 |$$

Accepted Answer

A)  $f ( x ) = x , g ( x ) = 7 x + 4$ 
B)  $f ( x ) = - | x | , g ( x ) = 7 x + 4$ 
C)  $f ( x ) = | - x | , g ( x ) = 7 x - 4$ 
D)  $f ( x ) = | x | , g ( x ) = 7 x + 4$ 
A)  $f ( x ) = x , g ( x ) = 7 x + 4$ 
B)  $f ( x ) = - | x | , g ( x ) = 7 x + 4$ 
C)  $f ( x ) = | - x | , g ( x ) = 7 x - 4$ 
D)  $f ( x ) = | x | , g ( x ) = 7 x + 4$

Question 12

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval.
-$$\sin x = - \frac { \sqrt { 5 } } { 3 } , \quad x \text { in } \left[ - \frac { \pi } { 2 } , 0 \right]$$

Accepted Answer

A)  $\cos x = - \frac { 2 } { 3 } , \tan x = \frac { \sqrt { 5 } } { 2 }$ 
B)  $\cos x = - \frac { 2 } { 3 } , \tan x = - \frac { \sqrt { 5 } } { 2 }$ 
C)  $\cos x = \frac { 2 } { 3 } , \tan x = \frac { \sqrt { 5 } } { 2 }$ 
D)  $\cos x = \frac { 2 } { 3 } , \tan x = - \frac { \sqrt { 5 } } { 2 }$ 
A)  $\cos x = - \frac { 2 } { 3 } , \tan x = \frac { \sqrt { 5 } } { 2 }$ 
B)  $\cos x = - \frac { 2 } { 3 } , \tan x = - \frac { \sqrt { 5 } } { 2 }$ 
C)  $\cos x = \frac { 2 } { 3 } , \tan x = \frac { \sqrt { 5 } } { 2 }$ 
D)  $\cos x = \frac { 2 } { 3 } , \tan x = - \frac { \sqrt { 5 } } { 2 }$

Question 13

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 14

Find the domain and range of the function.
-$f ( x ) = 5 - x ^ { 2 }$

Accepted Answer

A)  D: $( - \infty , 5 ] , \mathrm { R } : ( - \infty , \infty )$ 
B)  D: $( - \infty , \infty ) , \mathrm { R } : ( - \infty , 5 ]$ 
C)  D: $( - \infty , \infty )$, R: $[ 5 , \infty )$ 
D)  D: $( - \infty , \infty ) , \mathrm { R } : ( - \infty , \infty )$ 
A)  D: $( - \infty , 5 ] , \mathrm { R } : ( - \infty , \infty )$ 
B)  D: $( - \infty , \infty ) , \mathrm { R } : ( - \infty , 5 ]$ 
C)  D: $( - \infty , \infty )$, R: $[ 5 , \infty )$ 
D)  D: $( - \infty , \infty ) , \mathrm { R } : ( - \infty , \infty )$

Question 15

Simplify the expression.
-$5 \ln \sqrt [ 5 ] { \mathrm { e } }$

Accepted Answer

A)  $\frac { 1 } { 5 }$ 
B)  e 
C)  1 
D)  5 
A)  $\frac { 1 } { 5 }$ 
B)  e 
C)  1 
D)  5

Question 16

Solve the problem.
-If $f ( x ) = \sqrt { x } , g ( x ) = \frac { x } { 3 }$, and $h ( x ) = 3 x + 6$, find $h ( g ( f ( x ) ) )$.

Accepted Answer

A)  $3 \sqrt { x } + 6$ 
B)  $\sqrt { x + 2 }$ 
C)  $\sqrt { x } + 2$ 
D)  $\sqrt { x } + 6$ 
A)  $3 \sqrt { x } + 6$ 
B)  $\sqrt { x + 2 }$ 
C)  $\sqrt { x } + 2$ 
D)  $\sqrt { x } + 6$

Question 17

Find the domain and range of the inverse of the given function.
-$$f ( x ) = x ^ { 2 } + 3 , x \geq 0$$

Accepted Answer

A)  Domain: $[ 3 , \infty )$; range: $[ 0 , \infty )$ 
B)  Domain and range: all real numbers 
C)  Domain: $( - \infty , 0 ]$; range: $( - \infty , 3 ]$ 
D)  Domain: $[ 0 , \infty )$; range: $[ 3 , \infty )$ 
A)  Domain: $[ 3 , \infty )$; range: $[ 0 , \infty )$ 
B)  Domain and range: all real numbers 
C)  Domain: $( - \infty , 0 ]$; range: $( - \infty , 3 ]$ 
D)  Domain: $[ 0 , \infty )$; range: $[ 3 , \infty )$

Question 18

Rewrite the ratio as a ratio of natural logarithms and simplify.
-$\frac { \log _ { 2 } x } { \log _ { 16 } x }$

Accepted Answer

A)  $\frac { 1 } { 2 ^ { 3 } }$ 
B)  $2 ^ { 3 }$ 
C)  $\ln 4$ 
D)  4 
A)  $\frac { 1 } { 2 ^ { 3 } }$ 
B)  $2 ^ { 3 }$ 
C)  $\ln 4$ 
D)  4

Question 19

Find the exact value of the trigonometric function. Do not use a calculator or tables.
-$$\tan \left( \frac { 3 \pi } { 2 } \right)$$

Accepted Answer

A)  0 
B)  -1 
C)  1 
D)  Undefined 
A)  0 
B)  -1 
C)  1 
D)  Undefined

Question 20

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

Accepted Answer

A) True 
 B)False

Determine if the function is even, odd, or neither. - $h ( t ) = \sqrt { t ^ { 2 } - 6 }$

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

Express the following logarithm as specified. - $\frac { \ln 35 + \ln ( 1 / 7 ) } { \ln 625 }$ in terms of $\ln 5$ and $\ln 7$

Rewrite the ratio as a ratio of natural logarithms and simplify. - $\frac { \log _ { 10 } x } { \log _ { 11 } x }$

State the domain and range of the function. - $f ( x ) = 2 ^ { - x } + 2$

Use the appropriate addition formula to find the exact value of the expression. - $\tan \left( \frac { 13 \pi } { 12 } \right)$

Find the exact value of the trigonometric function. Do not use a calculator or tables. - $\tan \left( \frac { 4 \pi } { 3 } \right)$

Provide an appropriate response. -Find the inverse of the function $f ( x ) = x + 5$ . How is the graph of $f ^ { - 1 }$ related to the graph of $f$ ?

Find the formula for the function. -Express the length d of a square's diagonal as a function of its side length x.

Graph the function. - $y-4=x^{2 / 3}$ $Graph the function. - y-4=x^{2 / 3}$

Express the given function as a composite of functions f and g such that y $y = f ( g ( x ) )$ - $y = | 7 x + 4 |$

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval. - $\sin x = - \frac { \sqrt { 5 } } { 3 } , \quad x \text { in } \left[ - \frac { \pi } { 2 } , 0 \right]$

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

Find the domain and range of the function. - $f ( x ) = 5 - x ^ { 2 }$

Simplify the expression. - $5 \ln \sqrt [ 5 ] { \mathrm { e } }$

Solve the problem. -If $f ( x ) = \sqrt { x } , g ( x ) = \frac { x } { 3 }$ , and $h ( x ) = 3 x + 6$ , find $h ( g ( f ( x ) ) )$ .

Find the domain and range of the inverse of the given function. - $f ( x ) = x ^ { 2 } + 3 , x \geq 0$

Rewrite the ratio as a ratio of natural logarithms and simplify. - $\frac { \log _ { 2 } x } { \log _ { 16 } x }$

Find the exact value of the trigonometric function. Do not use a calculator or tables. - $\tan \left( \frac { 3 \pi } { 2 } \right)$

Determine from its graph if the function is one-to-one. - $f ( x ) = \left\{ \begin{array} { l l } x + 5 , & x > 0 \\4 , & x \leq 0\end{array} \right.$

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

Determine if the function is even, odd, or neither. - h(t)=t2−6h ( t ) = \sqrt { t ^ { 2 } - 6 }h(t)=t2−6​

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

Express the following logarithm as specified. - ln⁡35+ln⁡(1/7)ln⁡625\frac { \ln 35 + \ln ( 1 / 7 ) } { \ln 625 }ln625ln35+ln(1/7)​ in terms of ln⁡5\ln 5ln5 and ln⁡7\ln 7ln7

Rewrite the ratio as a ratio of natural logarithms and simplify. - log⁡10xlog⁡11x\frac { \log _ { 10 } x } { \log _ { 11 } x }log11​xlog10​x​

State the domain and range of the function. - f(x)=2−x+2f ( x ) = 2 ^ { - x } + 2f(x)=2−x+2

Use the appropriate addition formula to find the exact value of the expression. - tan⁡(13π12)\tan \left( \frac { 13 \pi } { 12 } \right)tan(1213π​)

Find the exact value of the trigonometric function. Do not use a calculator or tables. - tan⁡(4π3)\tan \left( \frac { 4 \pi } { 3 } \right)tan(34π​)

Provide an appropriate response. -Find the inverse of the function f(x)=x+5f ( x ) = x + 5f(x)=x+5 . How is the graph of f−1f ^ { - 1 }f−1 related to the graph of fff ?