Question 1

Determine whether the graph is the graph of a function.
-

Accepted Answer

A)  $Y e s$ 
B)  No 
A)  $Y e s$ 
B)  No

Question 2

Consider the functions f and g as shown in the graph. Sketch the graph of the indicated sum or difference of functions.
-Graph $g$ - f.

Accepted Answer

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

Question 3

Graph the function on your calculator to determine the domain and range from the graph.
-$$g ( x ) = \ln ( x - 7 )$$

Accepted Answer

A)  Domain: $( 7 , \infty )$; range: $( - \infty , \infty )$ 
B)  Domain: $[ 7 , \infty )$; range: $( - \infty , \infty )$ 
C)  Domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
D)  Domain: $( - \infty , \infty )$; range: $( 7 , \infty )$ 
A)  Domain: $( 7 , \infty )$; range: $( - \infty , \infty )$ 
B)  Domain: $[ 7 , \infty )$; range: $( - \infty , \infty )$ 
C)  Domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
D)  Domain: $( - \infty , \infty )$; range: $( 7 , \infty )$

Question 4

Solve the problem.
-Determine graphically the local maximum and local minimum of

Accepted Answer

A)  Local maximum: $ -2 $; local minimum: $ -\infty $ 
B)  No local maximum; local minimum: $ -2 $ 
C)  Local maximum: 0; no local minimum 
D)  Local maximum: $ -2 $; no local minimum 
A)  Local maximum: $ -2 $; local minimum: $ -\infty $ 
B)  No local maximum; local minimum: $ -2 $ 
C)  Local maximum: 0; no local minimum 
D)  Local maximum: $ -2 $; no local minimum

Question 5

Determine if the function is bounded above, bounded below, bounded on its domain, or unbounded on its domain.
-$$y = 9 x - x ^ { 3 }$$

Accepted Answer

A)  Bounded below 
B)  Bounded above 
C)  Bounded 
D)  Unbounded 
A)  Bounded below 
B)  Bounded above 
C)  Bounded 
D)  Unbounded

Question 6

Choose the one alternative that best completes the statement or answers the question.
Solve the problem.
-Let $\mathrm { f } ( \mathrm { x } )$ compute the time in hours to travel $x$ miles at 36 miles per hour. What is the interpretation the solution of $\mathrm { f } ^ { - 1 } ( \mathrm { x } ) = 8$ ?

Accepted Answer

A)  The hours taken to travel 8 miles 
B)  The miles traveled in 8 hours 
C)  The hours taken to travel 36 miles 
D)  The miles traveled in 36 hours 
A)  The hours taken to travel 8 miles 
B)  The miles traveled in 8 hours 
C)  The hours taken to travel 36 miles 
D)  The miles traveled in 36 hours

Question 7

Find the (x,y) pair for the value of the parameter.
-$x = - 6 t - 8$ and $y = 14 - t$ for $t = - 1$

Accepted Answer

A)  $( - 2,15 )$ 
B)  $( 6,14 )$ 
C)  $( 15 , - 2 )$ 
D)  $( 6,1 )$ 
A)  $( - 2,15 )$ 
B)  $( 6,14 )$ 
C)  $( 15 , - 2 )$ 
D)  $( 6,1 )$

Question 8

Perform the requested operation or operations. Find the domain of each.
-$f ( x ) = \sqrt { 6 x + 6 } , g ( x ) = \sqrt { 6 x - 6 }$ Find $( f + g ) ( x )$

Accepted Answer

A)  $\sqrt { 12 x }$; domain: $[ 0 , \infty )$ 
B)  $x \sqrt { 12 }$; domain: $( - \infty , \infty )$ 
C)  $6 x$; domain: $( - \infty , \infty )$ 
D)  $\sqrt { 6 x + 6 } + \sqrt { 6 x - 6 }$; domain: $[ 1 , \infty )$ 
A)  $\sqrt { 12 x }$; domain: $[ 0 , \infty )$ 
B)  $x \sqrt { 12 }$; domain: $( - \infty , \infty )$ 
C)  $6 x$; domain: $( - \infty , \infty )$ 
D)  $\sqrt { 6 x + 6 } + \sqrt { 6 x - 6 }$; domain: $[ 1 , \infty )$

Question 9

Use an equation to solve the problem.
-Joe Pearlman received a $2.75 \%$ pay decrease. His salary after the decrease was $\$ 36,955$. What was his salary before the decrease?

Accepted Answer

A)  $\$ 37,997.25$ 
B)  $\$ 37,999.725$ 
C)  $\$ 38,000$ 
D)  $\$ 39,045$ 
A)  $\$ 37,997.25$ 
B)  $\$ 37,999.725$ 
C)  $\$ 38,000$ 
D)  $\$ 39,045$

Question 10

Find the asymptote(s) of the given function.
-$g ( x ) = \frac { x ^ { 2 } + 1 x - 3 } { x - 3 }$ horizontal asymptotes(s)

Accepted Answer

A)  $y = - 1$ 
B)  None 
C)  $\mathrm { y } = 3$ 
D)  $\mathrm { y } = 9$ 
A)  $y = - 1$ 
B)  None 
C)  $\mathrm { y } = 3$ 
D)  $\mathrm { y } = 9$

Question 11

Describe how to transform the graph of f into the graph of g.
-$$f ( x ) = x ^ { 5 } \text { and } g ( x ) = ( 5 x ) ^ { 5 }$$

Accepted Answer

A)  Horizontally shrink the graph of $f$ by a factor of $\frac { 1 } { 5 }$. 
B)  Vertically shrink the graph of $\mathrm { f }$ by a factor of $\frac { 1 } { 5 }$. 
C)  Vertically stretch the graph of $f$ by a factor of 5 . 
D)  Horizontally stretch the graph of $f$ by a factor of 5 . 
A)  Horizontally shrink the graph of $f$ by a factor of $\frac { 1 } { 5 }$. 
B)  Vertically shrink the graph of $\mathrm { f }$ by a factor of $\frac { 1 } { 5 }$. 
C)  Vertically stretch the graph of $f$ by a factor of 5 . 
D)  Horizontally stretch the graph of $f$ by a factor of 5 .

Question 12

Write the specified quantity as a function of the specified variable.
-The base of an isosceles triangle is a fourth as long as the two equal sides. Write the area of the triangle as a function of the length of the base.

Accepted Answer

A)  $A = \frac { \sqrt { 15 } } { 4 } b ^ { 2 }$ 
B)  $A = \frac { 63 } { 8 } b ^ { 3 }$ 
C)  $A = 2 b ^ { 2 }$ 
D)  $A = \frac { 3 \sqrt { 7 } } { 4 } b ^ { 2 }$ 
A)  $A = \frac { \sqrt { 15 } } { 4 } b ^ { 2 }$ 
B)  $A = \frac { 63 } { 8 } b ^ { 3 }$ 
C)  $A = 2 b ^ { 2 }$ 
D)  $A = \frac { 3 \sqrt { 7 } } { 4 } b ^ { 2 }$

Question 13

Find the domain of the given function.
-$$f ( x ) = - 3$$

Accepted Answer

A)  $[ - 3,3 ]$ 
B)  All real numbers 
C)  $( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
D)  $[ 0 , \infty )$ 
A)  $[ - 3,3 ]$ 
B)  All real numbers 
C)  $( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
D)  $[ 0 , \infty )$

Question 14

Solve the equation algebraically.
-$x - \sqrt { 10 x - 25 } = 0$

Accepted Answer

A)  $- 25 ; 1$ 
B)  $25 ; - 1$ 
C)  $- 5$ 
D)  5 
A)  $- 25 ; 1$ 
B)  $25 ; - 1$ 
C)  $- 5$ 
D)  5

Question 15

Determine algebraically whether the function is even, odd, or neither even nor odd.
-$$f ( x ) = 4 x ^ { 5 } - 3 x ^ { 3 }$$

Accepted Answer

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

Question 16

Fill in the blanks to complete the statement.
-The graph of $y = - \frac { 1 } { 7 } \sqrt [ 3 ] { x + 9 }$ can be obtained from the graph of $y = \sqrt [ 3 ] { x }$ by shifting    units to   , vertically shrinking by a factor   , and then reflecting across   -axis.

Accepted Answer

A)  $9 ;$ right; $1 / 7 ; x$ 
B)  9 ; right; $- 1 / 7 ; y$ 
C)  $1 / 7$; right; 9 ; $\mathrm { y }$ 
D)  $9 ;$ left; $1 / 7 ; x$ 
A)  $9 ;$ right; $1 / 7 ; x$ 
B)  9 ; right; $- 1 / 7 ; y$ 
C)  $1 / 7$; right; 9 ; $\mathrm { y }$ 
D)  $9 ;$ left; $1 / 7 ; x$

Question 17

Find a direct relationship between x and y.
-$x = 5 \sqrt { t }$ and $y = 8 t - 4$

Accepted Answer

A)  $y = 200 x ^ { 2 } - 4$ 
B)  $y = \frac { 8 } { 5 } x - 4$ 
C)  $y = \frac { 8 } { 25 } x ^ { 2 } - 4$ 
D)  $y = 8 \sqrt { 5 } x - 4$ 
A)  $y = 200 x ^ { 2 } - 4$ 
B)  $y = \frac { 8 } { 5 } x - 4$ 
C)  $y = \frac { 8 } { 25 } x ^ { 2 } - 4$ 
D)  $y = 8 \sqrt { 5 } x - 4$

Question 18

Identify intervals on which the function is increasing, decreasing, or constant.
-$$g ( x ) = 3 - ( x + 8 ) ^ { 2 }$$

Accepted Answer

A)  Decreasing: $( - 8 , \infty )$; decreasing: $( - \infty , - 8 )$ 
B)  Increasing: $( - \infty , 8 )$; decreasing: $( 8 , \infty )$; 
C)  Increasing: $( 8 , \infty )$; decreasing: $( - \infty , 8 )$ 
D)  Increasing: $( - \infty , - 8 )$; decreasing: $( - 8 , \infty )$ 
A)  Decreasing: $( - 8 , \infty )$; decreasing: $( - \infty , - 8 )$ 
B)  Increasing: $( - \infty , 8 )$; decreasing: $( 8 , \infty )$; 
C)  Increasing: $( 8 , \infty )$; decreasing: $( - \infty , 8 )$ 
D)  Increasing: $( - \infty , - 8 )$; decreasing: $( - 8 , \infty )$

Question 19

Use an equation to solve the problem.
-A construction company builds a swimming pool with a perimeter of $50 \mathrm {~m}$. The length is $3 \mathrm {~m}$ more than the width. Find the dimensions of the swimming pool?

Accepted Answer

A)  $19 \mathrm {~m} \times 11 \mathrm {~m}$ 
B)  $9 \mathrm {~m} \times 11 \mathrm {~m}$ 
C)  $14 \mathrm {~m} \times 3 \mathrm {~m}$ 
D)  $14 \mathrm {~m} \times 11 \mathrm {~m}$ 
A)  $19 \mathrm {~m} \times 11 \mathrm {~m}$ 
B)  $9 \mathrm {~m} \times 11 \mathrm {~m}$ 
C)  $14 \mathrm {~m} \times 3 \mathrm {~m}$ 
D)  $14 \mathrm {~m} \times 11 \mathrm {~m}$

Question 20

Determine algebraically whether the function is even, odd, or neither even nor odd.
-$$f ( x ) = - 4$$

Accepted Answer

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

Determine whether the graph is the graph of a function. -

Consider the functions f and g as shown in the graph. Sketch the graph of the indicated sum or difference of functions. -Graph $g$ - f.

Graph the function on your calculator to determine the domain and range from the graph. - $g ( x ) = \ln ( x - 7 )$

Solve the problem. -Determine graphically the local maximum and local minimum of

Determine if the function is bounded above, bounded below, bounded on its domain, or unbounded on its domain. - $y = 9 x - x ^ { 3 }$

Find the (x,y) pair for the value of the parameter. - $x = - 6 t - 8$ and $y = 14 - t$ for $t = - 1$

Perform the requested operation or operations. Find the domain of each. - $f ( x ) = \sqrt { 6 x + 6 } , g ( x ) = \sqrt { 6 x - 6 }$ Find $( f + g ) ( x )$

Use an equation to solve the problem. -Joe Pearlman received a $2.75 \%$ pay decrease. His salary after the decrease was $\$ 36,955$ . What was his salary before the decrease?

Find the asymptote(s) of the given function. - $g ( x ) = \frac { x ^ { 2 } + 1 x - 3 } { x - 3 }$ horizontal asymptotes(s)

Describe how to transform the graph of f into the graph of g. - $f ( x ) = x ^ { 5 } \text { and } g ( x ) = ( 5 x ) ^ { 5 }$

Write the specified quantity as a function of the specified variable. -The base of an isosceles triangle is a fourth as long as the two equal sides. Write the area of the triangle as a function of the length of the base.

Find the domain of the given function. - $f ( x ) = - 3$

Solve the equation algebraically. - $x - \sqrt { 10 x - 25 } = 0$

Determine algebraically whether the function is even, odd, or neither even nor odd. - $f ( x ) = 4 x ^ { 5 } - 3 x ^ { 3 }$

Find a direct relationship between x and y. - $x = 5 \sqrt { t }$ and $y = 8 t - 4$

Identify intervals on which the function is increasing, decreasing, or constant. - $g ( x ) = 3 - ( x + 8 ) ^ { 2 }$

Use an equation to solve the problem. -A construction company builds a swimming pool with a perimeter of $50 \mathrm {~m}$ . The length is $3 \mathrm {~m}$ more than the width. Find the dimensions of the swimming pool?

Determine algebraically whether the function is even, odd, or neither even nor odd. - $f ( x ) = - 4$

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 whether the graph is the graph of a function. -

Consider the functions f and g as shown in the graph. Sketch the graph of the indicated sum or difference of functions. -Graph ggg - f.

Graph the function on your calculator to determine the domain and range from the graph. - g(x)=ln⁡(x−7)g ( x ) = \ln ( x - 7 )g(x)=ln(x−7)

Solve the problem. -Determine graphically the local maximum and local minimum of

Determine if the function is bounded above, bounded below, bounded on its domain, or unbounded on its domain. - y=9x−x3y = 9 x - x ^ { 3 }y=9x−x3

Find the (x,y) pair for the value of the parameter. - x=−6t−8x = - 6 t - 8x=−6t−8 and y=14−ty = 14 - ty=14−t for t=−1t = - 1t=−1

Perform the requested operation or operations. Find the domain of each. - f(x)=6x+6,g(x)=6x−6f ( x ) = \sqrt { 6 x + 6 } , g ( x ) = \sqrt { 6 x - 6 }f(x)=6x+6​,g(x)=6x−6​ Find (f+g)(x)( f + g ) ( x )(f+g)(x)

Use an equation to solve the problem. -Joe Pearlman received a 2.75%2.75 \%2.75% pay decrease. His salary after the decrease was $36,955\$ 36,955$36,955 . What was his salary before the decrease?

Find the asymptote(s) of the given function. - g(x)=x2+1x−3x−3g ( x ) = \frac { x ^ { 2 } + 1 x - 3 } { x - 3 }g(x)=x−3x2+1x−3​ horizontal asymptotes(s)

Describe how to transform the graph of f into the graph of g. - f(x)=x5 and g(x)=(5x)5f ( x ) = x ^ { 5 } \text { and } g ( x ) = ( 5 x ) ^ { 5 }f(x)=x5 and g(x)=(5x)5