Question 1

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

Accepted Answer

A)  Increasing on $( - 1,0 )$ and $( 3,5 )$; Decreasing on $( 0,3 )$; Constant on $( - 5 , - 3 )$ 
B)  Increasing on $( - 2,0 )$ and $( 3,5 )$; Decreasing on $( 1,3 )$; Constant on $( - 5 , - 2 )$ 
C)  Increasing on $( - 2,0 )$ and $( 3,4 )$; Decreasing on $( - 5 , - 2 )$ and $( 1,3 )$ 
D)  Increasing on $( 1,3 )$; Decreasing on $( - 2,0 )$ and $( 3,5 )$; Constant on $( 2,5 )$ 
A)  Increasing on $( - 1,0 )$ and $( 3,5 )$; Decreasing on $( 0,3 )$; Constant on $( - 5 , - 3 )$ 
B)  Increasing on $( - 2,0 )$ and $( 3,5 )$; Decreasing on $( 1,3 )$; Constant on $( - 5 , - 2 )$ 
C)  Increasing on $( - 2,0 )$ and $( 3,4 )$; Decreasing on $( - 5 , - 2 )$ and $( 1,3 )$ 
D)  Increasing on $( 1,3 )$; Decreasing on $( - 2,0 )$ and $( 3,5 )$; Constant on $( 2,5 )$

Question 2

Choose the one alternative that best completes the statement or answers the question.
-What symmetry does the graph of $y = f ( x )$ exhibit?

Accepted Answer

A)  origin 
B)  $y$-axis 
C)  $x$-axis 
D)  no symmetry 
A)  origin 
B)  $y$-axis 
C)  $x$-axis 
D)  no symmetry

Question 3

Solve the problem.
-The following information pertains to a bakery which makes donuts.

Make a scatterplot of the data. Based upon the scatterplot, what type of function would best model the data?

Accepted Answer

A)  Constant function 
B)  Quadratic function 
C)  Linear function 
D)  All of the above 
A)  Constant function 
B)  Quadratic function 
C)  Linear function 
D)  All of the above

Question 4

Give the equation of the function g whose graph is described.
-The graph of $f ( x ) = | x |$ is reflected across the $y$-axis. This graph is then vertically stretched by a factor of $7.9$. Finally, the graph is shifted 8 units downward.

Accepted Answer

A)  $g ( x ) = 7.9 | - x | - 8$ 
B)  $g ( x ) = 8 | - x | - 7.9$ 
C)  $g ( x ) = 7.9 | - x | + 8$ 
D)  $g ( x ) = - 7.9 | x | - 8$ 
A)  $g ( x ) = 7.9 | - x | - 8$ 
B)  $g ( x ) = 8 | - x | - 7.9$ 
C)  $g ( x ) = 7.9 | - x | + 8$ 
D)  $g ( x ) = - 7.9 | x | - 8$

Question 5

Fill in the blanks to complete the statement.
-The graph of $y = 0.1 | x - 9 | + 8.5$ can be obtained by shifting   units to the   , vertically shrinking by a factor of    and then shifting    units in   direction.

Accepted Answer

A)  9 ; left; $0.1 ; 8.5$; upward 
B)  $0.1 ;$ left; $9 ; 8.5$; upward 
C)  $8.5$; right; $0.1 ; 9$; downward 
D)  9 ; right; 0.1; 8.5; upward 
A)  9 ; left; $0.1 ; 8.5$; upward 
B)  $0.1 ;$ left; $9 ; 8.5$; upward 
C)  $8.5$; right; $0.1 ; 9$; downward 
D)  9 ; right; 0.1; 8.5; upward

Question 6

Find the domain of the given function.
-$$f ( x ) = \frac { x } { x - 6 }$$

Accepted Answer

A)  $( - \infty , - 6 ) \cup ( - 6 , \infty )$ 
B)  All real numbers 
C)  $( - \infty , 6 ) \cup ( 6 , \infty )$ 
D)  $( 0 , \infty )$ 
A)  $( - \infty , - 6 ) \cup ( - 6 , \infty )$ 
B)  All real numbers 
C)  $( - \infty , 6 ) \cup ( 6 , \infty )$ 
D)  $( 0 , \infty )$

Question 7

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.
-$y_{1}=3 \sqrt{x}, y_{2}=3 \sqrt{x}+2$

Accepted Answer

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

Question 8

Choose the one alternative that best completes the statement or answers the question.
Graph the piecewise-defined function.
-$$g ( x ) = \left\{ \begin{array} { l } 
x ^ { 2 } - 4 , \text { if } x  1
\end{array} \right.$$

Accepted Answer

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

Question 9

Use an equation to solve the problem.
-On Monday, an investor bought 100 shares of stock. On Tuesday, the value of the shares went up $5 \%$. How much did the investor pay for the 100 shares if he sold them Wednesday morning for $\$ 1470.00$ ?

Accepted Answer

A)  $\$ 1543.50$ 
B)  $\$ 1420.00$ 
C)  $\$ 1450.00$ 
D)  $\$ 1400.00$ 
A)  $\$ 1543.50$ 
B)  $\$ 1420.00$ 
C)  $\$ 1450.00$ 
D)  $\$ 1400.00$

Question 10

Find the inverse of the function.
-$$f ( x ) = \sqrt { x + 4 }$$

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \sqrt { x - 4 }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = ( \mathrm { x } + 4 ) ^ { 2 }$ 
C)  Not a one-to-one function 
D)  $f - 1 ( x ) = x ^ { 2 } - 4 , x \geq 0$ 
A)  $f ^ { - 1 } ( x ) = \sqrt { x - 4 }$ 
B)  $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = ( \mathrm { x } + 4 ) ^ { 2 }$ 
C)  Not a one-to-one function 
D)  $f - 1 ( x ) = x ^ { 2 } - 4 , x \geq 0$

Question 11

Find a direct relationship between x and y.
-$$\mathrm { x } = \mathrm { t } - 4 \text { and } \mathrm { y } = \mathrm { t } ^ { 2 } + \mathrm { t }$$

Accepted Answer

A)  $y = x ^ { 2 } + 9 x + 20$ 
B)  $y = x ^ { 2 } + x + 20$ 
C)  $y = x ^ { 2 } - 7 x + 12$ 
D)  $y = x ^ { 2 } + x + 12$ 
A)  $y = x ^ { 2 } + 9 x + 20$ 
B)  $y = x ^ { 2 } + x + 20$ 
C)  $y = x ^ { 2 } - 7 x + 12$ 
D)  $y = x ^ { 2 } + x + 12$

Question 12

Determine algebraically whether the function is even, odd, or neither even nor odd.
-$$f ( x ) = 13 x - 8 | x |$$

Accepted Answer

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

Question 13

Find the (x,y) pair for the value of the parameter.
-$x = | t + 1 |$ and $y = \frac { 1 } { t ^ { 2 } }$ for $t = 2$

Accepted Answer

A)  $\left( 3 , \frac { 1 } { 4 } \right)$ 
B)  $\left( - 3 , \frac { 1 } { 4 } \right)$ 
C)  $\left( \frac { 1 } { 4 } , - 3 \right)$ 
D)  $\left( 1 , \frac { 1 } { 4 } \right)$ 
A)  $\left( 3 , \frac { 1 } { 4 } \right)$ 
B)  $\left( - 3 , \frac { 1 } { 4 } \right)$ 
C)  $\left( \frac { 1 } { 4 } , - 3 \right)$ 
D)  $\left( 1 , \frac { 1 } { 4 } \right)$

Question 14

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

Accepted Answer

A)  $( - \infty , 2 )$ 
B)  $( - \infty , \infty )$ 
C)  $[ 0 , \infty )$ 
D)  $[ 2 , \infty )$ 
A)  $( - \infty , 2 )$ 
B)  $( - \infty , \infty )$ 
C)  $[ 0 , \infty )$ 
D)  $[ 2 , \infty )$

Question 15

Perform the requested operation or operations.
-$$f ( x ) = f ( x ) = \frac { 1 } { x - 4 } ; g ( x ) = \sqrt { x }$$
Find $g ( f ( x ) )$.

Accepted Answer

A)  $g ( f ( x ) ) = \frac { \sqrt { x } } { x - 4 }$ 
B)  $g ( f ( x ) ) = ( x - 4 ) \sqrt { x }$ 
C)  $g ( f ( x ) ) = \sqrt { \frac { 1 } { x - 4 } }$ 
D)  $g ( f ( x ) ) = \frac { 1 } { \sqrt { x } - 4 }$ 
A)  $g ( f ( x ) ) = \frac { \sqrt { x } } { x - 4 }$ 
B)  $g ( f ( x ) ) = ( x - 4 ) \sqrt { x }$ 
C)  $g ( f ( x ) ) = \sqrt { \frac { 1 } { x - 4 } }$ 
D)  $g ( f ( x ) ) = \frac { 1 } { \sqrt { x } - 4 }$

Question 16

Graph the function on your calculator to determine the domain and range from the graph.
-$$q ( x ) = \sin ( x ) + 2$$

Accepted Answer

A)  Domain: $( - \infty , \infty )$; range: $[ - 1,1 ]$ 
B)  Domain: $[ 1,3 ]$; range: $( - \infty , \infty )$ 
C)  Domain: $( - \infty , \infty )$; range: $( 1,3 )$ 
D)  Domain: $( - \infty , \infty )$; range: $[ 1,3 ]$ 
A)  Domain: $( - \infty , \infty )$; range: $[ - 1,1 ]$ 
B)  Domain: $[ 1,3 ]$; range: $( - \infty , \infty )$ 
C)  Domain: $( - \infty , \infty )$; range: $( 1,3 )$ 
D)  Domain: $( - \infty , \infty )$; range: $[ 1,3 ]$

Question 17

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

Accepted Answer

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

Question 18

Determine algebraically whether the function is even, odd, or neither even nor odd.
-$$f ( x ) = \frac { 28 } { x ^ { 2 } }$$

Accepted Answer

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

Question 19

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.
-$$f ( x ) = \frac { x ^ { 4 } + 2 x } { x }$$

Accepted Answer

A) 
 
Yes; non-removable 
B)

No 
C) 
 
No 
D) 
 
Yes; removable 
A) 
 
Yes; non-removable 
B)

No 
C) 
 
No 
D) 
 
Yes; removable

Question 20

Find the domain of the given function.
-$$f ( x ) = \frac { x } { x ^ { 2 } + 3 x }$$

Accepted Answer

A)  $( - \infty , 0 ) \cup ( 0,3 ) \cup ( 3 , \infty )$ 
B)  $( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
C)  $( - \infty , - 3 ) \cup ( - 3,0 ) \cup ( 0 , \infty )$ 
D)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
A)  $( - \infty , 0 ) \cup ( 0,3 ) \cup ( 3 , \infty )$ 
B)  $( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
C)  $( - \infty , - 3 ) \cup ( - 3,0 ) \cup ( 0 , \infty )$ 
D)  $( - \infty , 0 ) \cup ( 0 , \infty )$

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

Choose the one alternative that best completes the statement or answers the question. -What symmetry does the graph of $y = f ( x )$ exhibit?

Solve the problem. -The following information pertains to a bakery which makes donuts. Make a scatterplot of the data. Based upon the scatterplot, what type of function would best model the data?

Give the equation of the function g whose graph is described. -The graph of $f ( x ) = | x |$ is reflected across the $y$ -axis. This graph is then vertically stretched by a factor of $7.9$ . Finally, the graph is shifted 8 units downward.

Find the domain of the given function. - $f ( x ) = \frac { x } { x - 6 }$

Use an equation to solve the problem. -On Monday, an investor bought 100 shares of stock. On Tuesday, the value of the shares went up $5 \%$ . How much did the investor pay for the 100 shares if he sold them Wednesday morning for $\$ 1470.00$ ?

Find the inverse of the function. - $f ( x ) = \sqrt { x + 4 }$

Find a direct relationship between x and y. - $\mathrm { x } = \mathrm { t } - 4 \text { and } \mathrm { y } = \mathrm { t } ^ { 2 } + \mathrm { t }$

Determine algebraically whether the function is even, odd, or neither even nor odd. - $f ( x ) = 13 x - 8 | x |$

Find the (x,y) pair for the value of the parameter. - $x = | t + 1 |$ and $y = \frac { 1 } { t ^ { 2 } }$ for $t = 2$

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

Perform the requested operation or operations. - $f ( x ) = f ( x ) = \frac { 1 } { x - 4 } ; g ( x ) = \sqrt { x }$ Find $g ( f ( x ) )$ .

Graph the function on your calculator to determine the domain and range from the graph. - $q ( x ) = \sin ( x ) + 2$

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. - $f ( x ) = \frac { 28 } { x ^ { 2 } }$

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. - $f ( x ) = \frac { x ^ { 4 } + 2 x } { x }$

Find the domain of the given function. - $f ( x ) = \frac { x } { x ^ { 2 } + 3 x }$

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 1: Functions and Graphs

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

Choose the one alternative that best completes the statement or answers the question. -What symmetry does the graph of y=f(x)y = f ( x )y=f(x) exhibit?

Solve the problem. -The following information pertains to a bakery which makes donuts. Make a scatterplot of the data. Based upon the scatterplot, what type of function would best model the data?

Give the equation of the function g whose graph is described. -The graph of f(x)=∣x∣f ( x ) = | x |f(x)=∣x∣ is reflected across the yyy -axis. This graph is then vertically stretched by a factor of 7.97.97.9 . Finally, the graph is shifted 8 units downward.

Find the domain of the given function. - f(x)=xx−6f ( x ) = \frac { x } { x - 6 }f(x)=x−6x​

Use an equation to solve the problem. -On Monday, an investor bought 100 shares of stock. On Tuesday, the value of the shares went up 5%5 \%5% . How much did the investor pay for the 100 shares if he sold them Wednesday morning for $1470.00\$ 1470.00$1470.00 ?

Find the inverse of the function. - f(x)=x+4f ( x ) = \sqrt { x + 4 }f(x)=x+4​

Find a direct relationship between x and y. - x=t−4 and y=t2+t\mathrm { x } = \mathrm { t } - 4 \text { and } \mathrm { y } = \mathrm { t } ^ { 2 } + \mathrm { t }x=t−4 and y=t2+t

Determine algebraically whether the function is even, odd, or neither even nor odd. - f(x)=13x−8∣x∣f ( x ) = 13 x - 8 | x |f(x)=13x−8∣x∣

Find the (x,y) pair for the value of the parameter. - x=∣t+1∣x = | t + 1 |x=∣t+1∣ and y=1t2y = \frac { 1 } { t ^ { 2 } }y=t21​ for t=2t = 2t=2

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

Perform the requested operation or operations. - f(x)=f(x)=1x−4;g(x)=xf ( x ) = f ( x ) = \frac { 1 } { x - 4 } ; g ( x ) = \sqrt { x }f(x)=f(x)=x−41​;g(x)=x​ Find g(f(x))g ( f ( x ) )g(f(x)) .

Graph the function on your calculator to determine the domain and range from the graph. - q(x)=sin⁡(x)+2q ( x ) = \sin ( x ) + 2q(x)=sin(x)+2

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)=28x2f ( x ) = \frac { 28 } { x ^ { 2 } }f(x)=x228​

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. - f(x)=x4+2xxf ( x ) = \frac { x ^ { 4 } + 2 x } { x }f(x)=xx4+2x​

Find the domain of the given function. - f(x)=xx2+3xf ( x ) = \frac { x } { x ^ { 2 } + 3 x }f(x)=x2+3xx​

Polynomial, Power, and Rational Functions

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Choose the one alternative that best completes the statement or answers the question. -What symmetry does the graph of $y = f ( x )$ exhibit?

Give the equation of the function g whose graph is described. -The graph of $f ( x ) = | x |$ is reflected across the $y$ -axis. This graph is then vertically stretched by a factor of $7.9$ . Finally, the graph is shifted 8 units downward.

Find the domain of the given function. - $f ( x ) = \frac { x } { x - 6 }$

Use an equation to solve the problem. -On Monday, an investor bought 100 shares of stock. On Tuesday, the value of the shares went up $5 \%$ . How much did the investor pay for the 100 shares if he sold them Wednesday morning for $\$ 1470.00$ ?

Find the inverse of the function. - $f ( x ) = \sqrt { x + 4 }$

Find a direct relationship between x and y. - $\mathrm { x } = \mathrm { t } - 4 \text { and } \mathrm { y } = \mathrm { t } ^ { 2 } + \mathrm { t }$

Determine algebraically whether the function is even, odd, or neither even nor odd. - $f ( x ) = 13 x - 8 | x |$

Find the (x,y) pair for the value of the parameter. - $x = | t + 1 |$ and $y = \frac { 1 } { t ^ { 2 } }$ for $t = 2$

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

Perform the requested operation or operations. - $f ( x ) = f ( x ) = \frac { 1 } { x - 4 } ; g ( x ) = \sqrt { x }$ Find $g ( f ( x ) )$ .

Graph the function on your calculator to determine the domain and range from the graph. - $q ( x ) = \sin ( x ) + 2$

Determine algebraically whether the function is even, odd, or neither even nor odd. - $f ( x ) = \frac { 28 } { x ^ { 2 } }$

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. - $f ( x ) = \frac { x ^ { 4 } + 2 x } { x }$

Find the domain of the given function. - $f ( x ) = \frac { x } { x ^ { 2 } + 3 x }$