Question 1

Select the correct graph of the given function. 
 $f ( x ) = ( x - 3 ) ^ { 3 } - 3$

Accepted Answer

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

Question 2

Find the inverse of the one-to-one function.

Y = 5x + 9

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \frac { x + 9 } { 5 }$ 
B)  $f ^ { - 1 } ( x ) = \frac { x - 9 } { 5 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { 5 } { x - 9 }$ 
D)  $f ^ { - 1 } ( x ) = \frac { x - 5 } { 9 }$ 
E) none of the above 
A)  $f ^ { - 1 } ( x ) = \frac { x + 9 } { 5 }$ 
B)  $f ^ { - 1 } ( x ) = \frac { x - 9 } { 5 }$ 
C)  $f ^ { - 1 } ( x ) = \frac { 5 } { x - 9 }$ 
D)  $f ^ { - 1 } ( x ) = \frac { x - 5 } { 9 }$ 
E) none of the above

Question 3

Find the coordinates of the vertices of the polygon in its new position. ​
Original coordinates of vertices: (-5, -3), (-3, 6), (-5, -4), (-4, -7)
Shift: three units to the right, four units upward
​

Accepted Answer

A) (-2, 1), (0, 10), (-2, 0), (-1, -3) 
B) (1, 1), (0, 10), (-2, 0), (-1, -3) 
C) (2, 1), (0, 10), (-2, 0), (-1, -3) 
D) (3, 1), (0, 10), (-2, 0), (-1, -3) 
E) (4, 1), (0, 10), (-2, 0), (-1, -3) 
A) (-2, 1), (0, 10), (-2, 0), (-1, -3) 
B) (1, 1), (0, 10), (-2, 0), (-1, -3) 
C) (2, 1), (0, 10), (-2, 0), (-1, -3) 
D) (3, 1), (0, 10), (-2, 0), (-1, -3) 
E) (4, 1), (0, 10), (-2, 0), (-1, -3)

Question 4

Plot the following points and find the distance between the points.  
(-5, 8), (7, 2)

Accepted Answer

A)     Distance: $6 \sqrt { 5 }$ 
B)     Distance: $6 \sqrt { 5 }$ 
C)    Distance: $6 \sqrt { 5 }$ 
D)    Distance: $6 \sqrt { 5 }$ 
E)     Distance: $6 \sqrt { 5 }$ 
A)     Distance: $6 \sqrt { 5 }$ 
B)     Distance: $6 \sqrt { 5 }$ 
C)    Distance: $6 \sqrt { 5 }$ 
D)    Distance: $6 \sqrt { 5 }$ 
E)     Distance: $6 \sqrt { 5 }$

Question 5

Find the distance between the two points (-3, -1) and (13, 29).

Accepted Answer

A) 65 
B) 68 
C) 102 
D) 31 
E) 34 
A) 65 
B) 68 
C) 102 
D) 31 
E) 34

Question 6

Create and complete a table to find the x and y coordinates of points that lie on the graph of the equation below.Plot at least 5 points along with the graph of the equation. $y = x + 2$

Accepted Answer

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

Question 7

Find the zeros of the function algebraically. 
 $f ( x ) = \sqrt { 16 x } - 1$

Accepted Answer

A) x = 0, 16 
B)  $x = \frac { 1 } { 16 }$ 
C)  $x = 0 , \sqrt { 16 }$ 
D)  $x = 0 , \pm \sqrt { 16 }$ 
E)  $x = 0 , \pm 16$ 
A) x = 0, 16 
B)  $x = \frac { 1 } { 16 }$ 
C)  $x = 0 , \sqrt { 16 }$ 
D)  $x = 0 , \pm \sqrt { 16 }$ 
E)  $x = 0 , \pm 16$

Question 8

Which graph represents the function
 $$f ( x ) = \left\{ \begin{array} { l } 
- 3 x , x < 0 \
x - 3 , x \geq 0
\end{array} \right.$$

Accepted Answer

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

Question 9

Determine which of the following point lies on the graph of the equation.
 $y = \sqrt { x + 62 }$

Accepted Answer

A) (2, 10) 
B) (2, 9) 
C) (2, 8) 
D) (9, 8) 
E) (3, 8) 
A) (2, 10) 
B) (2, 9) 
C) (2, 8) 
D) (9, 8) 
E) (3, 8)

Question 10

Determine whether the function has an inverse function.If it does, find the inverse function. f(x) = x2 + 5

Accepted Answer

A)  $f ^ { - 1 } ( x ) = \sqrt { x } + 5 , x \geq 0$ 
B)  $f ^ { - 1 } ( x ) = \sqrt { x - 5 }$ 
C)  $f ^ { - 1 } ( x ) = \sqrt { x } - 5$ 
D)  $f ^ { - 1 } ( x ) = \sqrt { x + 5 } , x \geq - 5$ 
E) No inverse function exists. 
A)  $f ^ { - 1 } ( x ) = \sqrt { x } + 5 , x \geq 0$ 
B)  $f ^ { - 1 } ( x ) = \sqrt { x - 5 }$ 
C)  $f ^ { - 1 } ( x ) = \sqrt { x } - 5$ 
D)  $f ^ { - 1 } ( x ) = \sqrt { x + 5 } , x \geq - 5$ 
E) No inverse function exists.

Question 11

Use the graph of $f ( x ) = x ^ { 3 }$ to write an equation for the function whose graph is shown.

Accepted Answer

A)  $y = - 5 + x ^ { 3 }$ 
B)  $y = - 5 - x ^ { 3 }$ 
C)  $y = - 6 + x ^ { 3 }$ 
D)  $y = - 4 + x ^ { 3 }$ 
E)  $y = - 4 - x ^ { 3 }$ 
A)  $y = - 5 + x ^ { 3 }$ 
B)  $y = - 5 - x ^ { 3 }$ 
C)  $y = - 6 + x ^ { 3 }$ 
D)  $y = - 4 + x ^ { 3 }$ 
E)  $y = - 4 - x ^ { 3 }$

Question 12

Select the graph of the function f(x) = [[x - 4]]. ​

Accepted Answer

A) ​   
B) ​   
C) ​   
D) ​   
E) ​   
A) ​   
B) ​   
C) ​   
D) ​   
E) ​

Question 13

The cost of sending an overnight package from Los Angeles to Miami is $26.40 for a package weighing up to but not including 1 pound and $3.25 for each additional pound or portion of a pound.A model for the total cost C (in dollars) of sending the package is ​
С = 26.40 + 3.25[[x]] , x > 0, where x is the weight in pounds.
​
Determine the cost of sending a package that weighs 5.25 pounds.
​

Accepted Answer

A) $45.65 
B) ​$44.65 
C) ​$43.65 
D) ​$46.65 
E) ​$42.65 
A) $45.65 
B) ​$44.65 
C) ​$43.65 
D) ​$46.65 
E) ​$42.65

Question 14

Find all real value of x such that f (x) = 0. $f ( x ) = \frac { - 9 x + 8 } { 5 }$

Accepted Answer

A) x = $\frac { 8 } { 9 }$ 
B) x = $\frac { 8 } { 45 }$ 
C) x = ± $\frac { 8 } { 9 }$ 
D) x = $- \frac { 8 } { 9 }$ 
E) x = ± $\frac { 8 } { 45 }$ 
A) x = $\frac { 8 } { 9 }$ 
B) x = $\frac { 8 } { 45 }$ 
C) x = ± $\frac { 8 } { 9 }$ 
D) x = $- \frac { 8 } { 9 }$ 
E) x = ± $\frac { 8 } { 45 }$

Question 15

Find the graph of the equation. ​
F (x) = | x - 4 |
​

Accepted Answer

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

Question 16

Graph the function.
 $y = [ [ 4 x ] ]$

Accepted Answer

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

Question 17

Sketch the graph of the equation $4 x ^ { 3 } + 4$ .

Accepted Answer

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

Question 18

The simple interest on an investment is directly proportional to the amount of the investment.By investing $5800 in a municipal bond, you obtained an interest payment of $221.25 after 1 year.Find a mathematical model that gives the interest I for this municipal bond after 1 year in terms of the amount invested P.(Round your answer to three decimal places.)

Accepted Answer

A)  $I = 26.215 P$ 
B)  $I = 221.25 P$ 
C)  $I = 0.038 P$ 
D)  $I = 1,283,250 P$ 
E)  $I = 5800 P$ 
A)  $I = 26.215 P$ 
B)  $I = 221.25 P$ 
C)  $I = 0.038 P$ 
D)  $I = 1,283,250 P$ 
E)  $I = 5800 P$

Question 19

Find the distance between the two points (10, 7) and (-5, 7). ​

Accepted Answer

A) 30 
B) 20 
C) 12 
D) 40 
E) 15 
A) 30 
B) 20 
C) 12 
D) 40 
E) 15

Question 20

Find a mathematical model representing the statement.(Determine the constant of proportionality.)  
Y is inversely proportional to x. $( y = 7 \text { when } x = 5 . )$

Accepted Answer

A)  $y = \frac { 5 } { x }$ 
B)  $y = \frac { x } { 35 }$ 
C)  $y = 35 x$ 
D)  $y = \frac { 35 } { x }$ 
E)  $y = \frac { 7 } { x }$ 
A)  $y = \frac { 5 } { x }$ 
B)  $y = \frac { x } { 35 }$ 
C)  $y = 35 x$ 
D)  $y = \frac { 35 } { x }$ 
E)  $y = \frac { 7 } { x }$

Select the correct graph of the given function. $f ( x ) = ( x - 3 ) ^ { 3 } - 3$

Find the inverse of the one-to-one function. Y = 5x + 9

Find the coordinates of the vertices of the polygon in its new position. Original coordinates of vertices: (-5, -3), (-3, 6), (-5, -4), (-4, -7) Shift: three units to the right, four units upward

Plot the following points and find the distance between the points. (-5, 8), (7, 2)

Find the distance between the two points (-3, -1) and (13, 29).

Create and complete a table to find the x and y coordinates of points that lie on the graph of the equation below.Plot at least 5 points along with the graph of the equation. $y = x + 2$

Find the zeros of the function algebraically. $f ( x ) = \sqrt { 16 x } - 1$

Which graph represents the function $f ( x ) = \left\{ \begin{array} { l } - 3 x , x < 0 \\x - 3 , x \geq 0\end{array} \right.$

Determine which of the following point lies on the graph of the equation. $y = \sqrt { x + 62 }$

Determine whether the function has an inverse function.If it does, find the inverse function. f(x) = x² + 5

Use the graph of $f ( x ) = x ^ { 3 }$ to write an equation for the function whose graph is shown. $Use the graph of f ( x ) = x ^ { 3 } to write an equation for the function whose graph is shown.$

Select the graph of the function f(x) = [[x - 4]].

Find all real value of x such that f (x) = 0. $f ( x ) = \frac { - 9 x + 8 } { 5 }$

Find the graph of the equation. F (x) = | x - 4 |

Graph the function. $y = [ [ 4 x ] ]$

Sketch the graph of the equation $4 x ^ { 3 } + 4$ .

Find the distance between the two points (10, 7) and (-5, 7).

Find a mathematical model representing the statement.(Determine the constant of proportionality.) Y is inversely proportional to x. $( y = 7 \text { when } x = 5 . )$

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Exam 1: Functions and Their Graphs

Select the correct graph of the given function. f(x)=(x−3)3−3f ( x ) = ( x - 3 ) ^ { 3 } - 3f(x)=(x−3)3−3

Find the inverse of the one-to-one function. Y = 5x + 9

Find the coordinates of the vertices of the polygon in its new position. ​ Original coordinates of vertices: (-5, -3), (-3, 6), (-5, -4), (-4, -7) Shift: three units to the right, four units upward ​

Plot the following points and find the distance between the points. (-5, 8), (7, 2)

Find the distance between the two points (-3, -1) and (13, 29).

Create and complete a table to find the x and y coordinates of points that lie on the graph of the equation below.Plot at least 5 points along with the graph of the equation. y=x+2y = x + 2y=x+2

Find the zeros of the function algebraically. f(x)=16x−1f ( x ) = \sqrt { 16 x } - 1f(x)=16x​−1

Which graph represents the function f(x)={−3x,x<0x−3,x≥0f ( x ) = \left\{ \begin{array} { l } - 3 x , x < 0 \\x - 3 , x \geq 0\end{array} \right.f(x)={−3x,x<0x−3,x≥0​

Determine which of the following point lies on the graph of the equation. y=x+62y = \sqrt { x + 62 }y=x+62​

Determine whether the function has an inverse function.If it does, find the inverse function. f(x) = x2 + 5

Use the graph of f(x)=x3f ( x ) = x ^ { 3 }f(x)=x3 to write an equation for the function whose graph is shown.

Select the graph of the function f(x) = [[x - 4]]. ​

Find all real value of x such that f (x) = 0. f(x)=−9x+85f ( x ) = \frac { - 9 x + 8 } { 5 }f(x)=5−9x+8​

Find the graph of the equation. ​ F (x) = | x - 4 | ​

Graph the function. y=[[4x]]y = [ [ 4 x ] ]y=[[4x]]

Sketch the graph of the equation 4x3+44 x ^ { 3 } + 44x3+4 .

Find the distance between the two points (10, 7) and (-5, 7). ​

Find a mathematical model representing the statement.(Determine the constant of proportionality.) Y is inversely proportional to x. (y=7 when x=5.)( y = 7 \text { when } x = 5 . )(y=7 when x=5.)

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Trigonometry

Analytic Trigonometry

Additional Topics In Trigonometery

Systems Of Equations and Inequalities

Matrices and Determinants

Sequences Series and Probability

Topics In Analytic Geometry

Analytic Geometry In Three Dimensions

Limits and An Introduction To Calculus

Filters

Select the correct graph of the given function. $f ( x ) = ( x - 3 ) ^ { 3 } - 3$

Find the coordinates of the vertices of the polygon in its new position. Original coordinates of vertices: (-5, -3), (-3, 6), (-5, -4), (-4, -7) Shift: three units to the right, four units upward

Create and complete a table to find the x and y coordinates of points that lie on the graph of the equation below.Plot at least 5 points along with the graph of the equation. $y = x + 2$

Find the zeros of the function algebraically. $f ( x ) = \sqrt { 16 x } - 1$

Which graph represents the function $f ( x ) = \left\{ \begin{array} { l } - 3 x , x < 0 \\x - 3 , x \geq 0\end{array} \right.$

Determine which of the following point lies on the graph of the equation. $y = \sqrt { x + 62 }$

Determine whether the function has an inverse function.If it does, find the inverse function. f(x) = x² + 5

Use the graph of $f ( x ) = x ^ { 3 }$ to write an equation for the function whose graph is shown. $Use the graph of f ( x ) = x ^ { 3 } to write an equation for the function whose graph is shown.$

Select the graph of the function f(x) = [[x - 4]].

Find all real value of x such that f (x) = 0. $f ( x ) = \frac { - 9 x + 8 } { 5 }$

Find the graph of the equation. F (x) = | x - 4 |

Graph the function. $y = [ [ 4 x ] ]$

Sketch the graph of the equation $4 x ^ { 3 } + 4$ .

Find the distance between the two points (10, 7) and (-5, 7).

Find a mathematical model representing the statement.(Determine the constant of proportionality.) Y is inversely proportional to x. $( y = 7 \text { when } x = 5 . )$