Question 1

Use a graphing calculator to solve the linear equation.
-$$( - 9 x + 8 ) + 4 = - 8 ( x + 9 )$$

Accepted Answer

A)  $\{ - 84 \}$ 
B)  $\{ - 76 \}$ 
C)  $\{ 84 \}$ 
D)  $\{ - 3 \}$ 
A)  $\{ - 84 \}$ 
B)  $\{ - 76 \}$ 
C)  $\{ 84 \}$ 
D)  $\{ - 3 \}$

Question 2

Give a rule for the piecewise-defined function. Then give the domain and range.
-$f(x)=\llbracket x+1]$

Accepted Answer

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

Question 3

Graph the point symmetric to the given point.
-Plot the point (7, 10), then plot the point that is symmetric to (7, 10) with respect to the y-axis.

Accepted Answer

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

Question 4

Find the requested function value.
-Find $( g \circ f ) ( 13 )$ when $f ( x ) = \frac { x - 3 } { 2 }$ and $g ( x ) = 3 x + 1$

Accepted Answer

A)  200 
B)  16 
C)  20 
D)  $\frac { 37 } { 2 }$ 
A)  200 
B)  16 
C)  20 
D)  $\frac { 37 } { 2 }$

Question 5

Find the average rate of change illustrated in the graph.
-The rate of return of certain investments increases as the risk factor of the investment increases. An investment with a risk factor of 2 has a rate of return of 5.0%. An investment with a risk factor of 25 has a rate of return of
24.0%. What is the average rate of change in return per unit of risk? Round to two decimal places.

Accepted Answer

A)  0.83% per unit risk 
B)  1.21% per unit risk 
C)  1.10% per unit risk 
D)  0.91% per unit risk 
A)  0.83% per unit risk 
B)  1.21% per unit risk 
C)  1.10% per unit risk 
D)  0.91% per unit risk

Question 6

Determine whether the three points are collinear.
-$( - 2,6 ) , ( - 4 , - 3 ) , ( 0,15 )$

Accepted Answer

A) True 
 B)False

Question 7

The figure below shows the graph of a functio $y = f ( x )$ e this graph to
-$$\text { Sketch the graph of } y = - \frac { 1 } { 2 } f ( x ) \text {. }$$

Accepted Answer

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

Question 8

Employees of a publishing company received an increase in salary of 3% plus a bonus of $700. Let S(x) represent the new salary in terms of the previous salary x. Find the value of S(15,000).

Accepted Answer

A)  $13,883 
B)  $20,200 
C)  $16,150 
D)  $15,700 
A)  $13,883 
B)  $20,200 
C)  $16,150 
D)  $15,700

Question 9

Find the center-radius form of the equation of the circle.
-center $( - 8 , - 7 )$, radius $\sqrt { 3 }$

Accepted Answer

A)  $( x - 8 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 3$ 
B)  $( x - 7 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 9$ 
C)  $( x + 7 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 9$ 
D)  $( x + 8 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 3$ 
A)  $( x - 8 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 3$ 
B)  $( x - 7 ) ^ { 2 } + ( y - 8 ) ^ { 2 } = 9$ 
C)  $( x + 7 ) ^ { 2 } + ( y + 8 ) ^ { 2 } = 9$ 
D)  $( x + 8 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 3$

Question 10

Use the tables to find $( \mathrm { fg } ) ( - 9 )$.

Accepted Answer

A)  $- 36$ 
B)  81 
C)  $- 24$ 
D)  $- 4$ 
A)  $- 36$ 
B)  81 
C)  $- 24$ 
D)  $- 4$

Question 11

Give a rule for the piecewise-defined function. Then give the domain and range.
-

Accepted Answer

A) $f ( x ) = \left\{ \begin{array} { l l } 5 & \text { if } x \leq 0 \ - x & \text { if } x > 0 \end{array} ; \right.$ Domain: $( \infty , \infty )$, Range: $( \infty , 0 ) \cup \{ 5 \}$ B) $f ( x ) = \left\{ \begin{array} { l } 5 \text { if } x < 0 \ x \text { if } x \geq 0 \end{array} ; \right.$ Domain: $( \infty , 0 ] \cup ( 5 )$, Range: $( \infty , \infty )$ C) $f ( x ) = \left\{ \begin{array} { l l } 5 & \text { if } x < 0 \ - 5 x & \text { if } x \geq 0 \end{array} ; \right.$ Domain: $( \infty , 0 ) \cup \{ 5 \}$, Range: $( \infty , \infty )$ D) $f ( x ) = \left\{ \begin{array} { l l } 5 & \text { if } x < 0 \ - x & \text { if } x \geq 0 \end{array} ; \right.$ Domain: $( \infty , \infty )$, Range: $( \infty , 0 ] \cup \{ 5 \}$ A) $f ( x ) = \left\{ \begin{array} { l l } 5 & \text { if } x \leq 0 \ - x & \text { if } x > 0 \end{array} ; \right.$ Domain: $( \infty , \infty )$, Range: $( \infty , 0 ) \cup \{ 5 \}$ B) $f ( x ) = \left\{ \begin{array} { l } 5 \text { if } x < 0 \ x \text { if } x \geq 0 \end{array} ; \right.$ Domain: $( \infty , 0 ] \cup ( 5 )$, Range: $( \infty , \infty )$ C) $f ( x ) = \left\{ \begin{array} { l l } 5 & \text { if } x < 0 \ - 5 x & \text { if } x \geq 0 \end{array} ; \right.$ Domain: $( \infty , 0 ) \cup \{ 5 \}$, Range: $( \infty , \infty )$ D) $f ( x ) = \left\{ \begin{array} { l l } 5 & \text { if } x < 0 \ - x & \text { if } x \geq 0 \end{array} ; \right.$ Domain: $( \infty , \infty )$, Range: $( \infty , 0 ] \cup \{ 5 \}$

Question 12

For the pair of functions, find the indicated sum, difference, product, or quotient.
-$$f ( x ) = 8 x + 1 , g ( x ) = 4 x - 2$$
Find $( f g ) ( x )$.

Accepted Answer

A)  $12 x ^ { 2 } - 12 x - 1$ 
B)  $32 x ^ { 2 } - 2$ 
C)  $32 x ^ { 2 } + 2 x - 2$ 
D)  $32 x ^ { 2 } - 12 x - 2$ 
A)  $12 x ^ { 2 } - 12 x - 1$ 
B)  $32 x ^ { 2 } - 2$ 
C)  $32 x ^ { 2 } + 2 x - 2$ 
D)  $32 x ^ { 2 } - 12 x - 2$

Question 13

Suppose that receiving stations $X , Y$, and $Z$ are located on a coordinate plane at the points $( 0,9 ) , ( - 12,17 )$, and $( - 8 , - 7 )$ respectively. The epicenter of an earthquake is determined to be 5 units from $X , 15$ units from $Y$, and 13 units from $Z$. Where on the coordinate plane is the epicenter located?

Accepted Answer

A)  at $( - 2,5 )$ 
B)  at $( - 4,7 )$ 
C)  at $( - 2,4 )$ 
D)  at $( - 3,5 )$ 
A)  at $( - 2,5 )$ 
B)  at $( - 4,7 )$ 
C)  at $( - 2,4 )$ 
D)  at $( - 3,5 )$

Question 14

Describe how the graph of the equation relates to the graph $$y = x ^ { 2 }$$
-$f ( x ) = - ( x + 6 ) ^ { 2 }$

Accepted Answer

A)  a translation 6 units to the left and a reflection across the x-axis 
B)  a translation 6 units to the right and a reflection across the y-axis 
C)  a translation 6 units up and a reflection across the x-axis 
D)  a translation 6 units to the right and a reflection across the x-axis 
A)  a translation 6 units to the left and a reflection across the x-axis 
B)  a translation 6 units to the right and a reflection across the y-axis 
C)  a translation 6 units up and a reflection across the x-axis 
D)  a translation 6 units to the right and a reflection across the x-axis

Question 15

Graph the circle.
-$x^{2}+y^{2}=25$

Accepted Answer

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

Question 16

Determine whether $$( f \circ g ) ( x ) = x \text { and whether } ( g \circ f ) ( x ) = x \text {. }$$
-$f ( x ) = x ^ { 2 } + 3 , g ( x ) = \sqrt { x } - 3$

Accepted Answer

A)  Yes, no 
B)  Yes, yes 
C)  No, yes 
D)  No, no 
A)  Yes, no 
B)  Yes, yes 
C)  No, yes 
D)  No, no

Question 17

Write all linear equations in slope-intercept form.
-The table lists the average annual cost (in dollars) of room and board at public four-year colleges in the city of Bookhaven for selected years. PUBLIC FOUR-YEAR COLLEGE ROOM AND BOARD

Determine a linear function $\mathrm { f }$ defined by $\mathrm { f } ( \mathrm { x } ) = \mathrm { mx } + \mathrm { b }$ that models the data using $( 1,1350 )$ and $( 6,3105 )$.

Accepted Answer

A)  $f ( x ) = 2851 - 1501 x$ 
B)  $f ( x ) = 351 x + 999$ 
C)  $f ( x ) = 999 x + 351$ 
D)  $f ( x ) = 1350$ 
A)  $f ( x ) = 2851 - 1501 x$ 
B)  $f ( x ) = 351 x + 999$ 
C)  $f ( x ) = 999 x + 351$ 
D)  $f ( x ) = 1350$

Question 18

Determine the largest open intervals of the domain over which the function is increasing, decreasing, and constant.
-

Accepted Answer

A)  Increasing $( - \infty , 0 )$; Decreasing $( - \infty , 0 )$ 
B)  Increasing $( - \infty , 0 )$; Decreasing $( 0 , \infty )$ 
C)  Increasing $( 0 , \infty )$; Decreasing $( - \infty , 0 )$ 
D)  Increasing $( - \infty , 0 )$; Decreasing $( 0 , - \infty )$ 
A)  Increasing $( - \infty , 0 )$; Decreasing $( - \infty , 0 )$ 
B)  Increasing $( - \infty , 0 )$; Decreasing $( 0 , \infty )$ 
C)  Increasing $( 0 , \infty )$; Decreasing $( - \infty , 0 )$ 
D)  Increasing $( - \infty , 0 )$; Decreasing $( 0 , - \infty )$

Question 19

Give the domain and range of the relation.
-$$y = ( x - 1 ) ^ { 2 } + 1$$

Accepted Answer

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

Question 20

Decide whether the relation defines a function.
-

Accepted Answer

A)  Function 
B)  Not a function 
A)  Function 
B)  Not a function

Use a graphing calculator to solve the linear equation. - $( - 9 x + 8 ) + 4 = - 8 ( x + 9 )$

Give a rule for the piecewise-defined function. Then give the domain and range. - $f(x)=\llbracket x+1]$ $Give a rule for the piecewise-defined function. Then give the domain and range. - f(x)=\llbracket x+1]$

Graph the point symmetric to the given point. -Plot the point (7, 10), then plot the point that is symmetric to (7, 10) with respect to the y-axis.

Find the requested function value. -Find $( g \circ f ) ( 13 )$ when $f ( x ) = \frac { x - 3 } { 2 }$ and $g ( x ) = 3 x + 1$

Determine whether the three points are collinear. - $( - 2,6 ) , ( - 4 , - 3 ) , ( 0,15 )$

Employees of a publishing company received an increase in salary of 3% plus a bonus of $700. Let S(x) represent the new salary in terms of the previous salary x. Find the value of S(15,000).

Find the center-radius form of the equation of the circle. -center $( - 8 , - 7 )$ , radius $\sqrt { 3 }$

Use the tables to find $( \mathrm { fg } ) ( - 9 )$ . $Use the tables to find ( \mathrm { fg } ) ( - 9 ) .$

Give a rule for the piecewise-defined function. Then give the domain and range. -

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = 8 x + 1 , g ( x ) = 4 x - 2$ Find $( f g ) ( x )$ .

Describe how the graph of the equation relates to the graph $y = x ^ { 2 }$ - $f ( x ) = - ( x + 6 ) ^ { 2 }$

Graph the circle. - $x^{2}+y^{2}=25$ $Graph the circle. - x^{2}+y^{2}=25$

Determine whether $( f \circ g ) ( x ) = x \text { and whether } ( g \circ f ) ( x ) = x \text {. }$ - $f ( x ) = x ^ { 2 } + 3 , g ( x ) = \sqrt { x } - 3$

Determine the largest open intervals of the domain over which the function is increasing, decreasing, and constant. -

Give the domain and range of the relation. - $y = ( x - 1 ) ^ { 2 } + 1$

Decide whether the relation defines a function. -

Review of Basic Concepts

Equations and Inequalities

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 3: Graphs and Functions

Use a graphing calculator to solve the linear equation. - (−9x+8)+4=−8(x+9)( - 9 x + 8 ) + 4 = - 8 ( x + 9 )(−9x+8)+4=−8(x+9)

Give a rule for the piecewise-defined function. Then give the domain and range. - f(x)=⟦x+1]f(x)=\llbracket x+1]f(x)=[[x+1]

Graph the point symmetric to the given point. -Plot the point (7, 10), then plot the point that is symmetric to (7, 10) with respect to the y-axis.

Find the requested function value. -Find (g∘f)(13)( g \circ f ) ( 13 )(g∘f)(13) when f(x)=x−32f ( x ) = \frac { x - 3 } { 2 }f(x)=2x−3​ and g(x)=3x+1g ( x ) = 3 x + 1g(x)=3x+1

Determine whether the three points are collinear. - (−2,6),(−4,−3),(0,15)( - 2,6 ) , ( - 4 , - 3 ) , ( 0,15 )(−2,6),(−4,−3),(0,15)

The figure below shows the graph of a functio y=f(x)y = f ( x )y=f(x) e this graph to - Sketch the graph of y=−12f(x). \text { Sketch the graph of } y = - \frac { 1 } { 2 } f ( x ) \text {. } Sketch the graph of y=−21​f(x).

Employees of a publishing company received an increase in salary of 3% plus a bonus of $700. Let S(x) represent the new salary in terms of the previous salary x. Find the value of S(15,000).

Find the center-radius form of the equation of the circle. -center (−8,−7)( - 8 , - 7 )(−8,−7) , radius 3\sqrt { 3 }3​

Use the tables to find (fg)(−9)( \mathrm { fg } ) ( - 9 )(fg)(−9) .

Give a rule for the piecewise-defined function. Then give the domain and range. -

For the pair of functions, find the indicated sum, difference, product, or quotient. - f(x)=8x+1,g(x)=4x−2f ( x ) = 8 x + 1 , g ( x ) = 4 x - 2f(x)=8x+1,g(x)=4x−2 Find (fg)(x)( f g ) ( x )(fg)(x) .

Describe how the graph of the equation relates to the graph y=x2y = x ^ { 2 }y=x2 - f(x)=−(x+6)2f ( x ) = - ( x + 6 ) ^ { 2 }f(x)=−(x+6)2

Graph the circle. - x2+y2=25x^{2}+y^{2}=25x2+y2=25

Determine whether (f∘g)(x)=x and whether (g∘f)(x)=x. ( f \circ g ) ( x ) = x \text { and whether } ( g \circ f ) ( x ) = x \text {. }(f∘g)(x)=x and whether (g∘f)(x)=x. - f(x)=x2+3,g(x)=x−3f ( x ) = x ^ { 2 } + 3 , g ( x ) = \sqrt { x } - 3f(x)=x2+3,g(x)=x​−3

Determine the largest open intervals of the domain over which the function is increasing, decreasing, and constant. -

Give the domain and range of the relation. - y=(x−1)2+1y = ( x - 1 ) ^ { 2 } + 1y=(x−1)2+1

Decide whether the relation defines a function. -

Review of Basic Concepts

Equations and Inequalities

Polynomials and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Use a graphing calculator to solve the linear equation. - $( - 9 x + 8 ) + 4 = - 8 ( x + 9 )$

Give a rule for the piecewise-defined function. Then give the domain and range. - $f(x)=\llbracket x+1]$ $Give a rule for the piecewise-defined function. Then give the domain and range. - f(x)=\llbracket x+1]$

Find the requested function value. -Find $( g \circ f ) ( 13 )$ when $f ( x ) = \frac { x - 3 } { 2 }$ and $g ( x ) = 3 x + 1$

Determine whether the three points are collinear. - $( - 2,6 ) , ( - 4 , - 3 ) , ( 0,15 )$

Find the center-radius form of the equation of the circle. -center $( - 8 , - 7 )$ , radius $\sqrt { 3 }$

Use the tables to find $( \mathrm { fg } ) ( - 9 )$ . $Use the tables to find ( \mathrm { fg } ) ( - 9 ) .$

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = 8 x + 1 , g ( x ) = 4 x - 2$ Find $( f g ) ( x )$ .

Describe how the graph of the equation relates to the graph $y = x ^ { 2 }$ - $f ( x ) = - ( x + 6 ) ^ { 2 }$

Graph the circle. - $x^{2}+y^{2}=25$ $Graph the circle. - x^{2}+y^{2}=25$

Determine whether $( f \circ g ) ( x ) = x \text { and whether } ( g \circ f ) ( x ) = x \text {. }$ - $f ( x ) = x ^ { 2 } + 3 , g ( x ) = \sqrt { x } - 3$

Give the domain and range of the relation. - $y = ( x - 1 ) ^ { 2 } + 1$