Question 1

Decide whether the relation defines a function.
-

Accepted Answer

A) $\text { Not a function }$ 
B)  Function 
A) $\text { Not a function }$ 
B)  Function

Question 2

Solve the problem.
-Use the graphs to find the value of $\left( \frac { f } { g } \right) ( 3 )$.

Accepted Answer

A)  undefined 
B)  1 
C)  $- 2$ 
D)  $- 1$ 
A)  undefined 
B)  1 
C)  $- 2$ 
D)  $- 1$

Question 3

Solve the problem.
-From April through December, the stock price of QRS Company had a roller coaster ride. The chart below indicates the price of the stock at the beginning of each month during that period.
Find the average rate of change in price per month between June and September. Round to the
Nearest cent.

Accepted Answer

A)  $\$ 12.00$ per month 
B)  $- \$ 8.00$ per month 
C)  $- \$ 12.00$ per month 
D)  $\$ 8.00$ per month 
A)  $\$ 12.00$ per month 
B)  $- \$ 8.00$ per month 
C)  $- \$ 12.00$ per month 
D)  $\$ 8.00$ per month

Question 4

Graph the function.
-$f(x)=(7 x)^{2}$

Accepted Answer

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

Question 5

Determine whether (f ∘ g)(x) = x and whether (g ∘ f)(x) = x.
-$$f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 }$$

Accepted Answer

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

Question 6

Compute and simplify the difference quotient $$\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$$
-$$f ( x ) = \frac { x - 8 } { x + 3 }$$

Accepted Answer

A)  $\frac { 11 } { ( x + h + 3 ) ( x + 3 ) }$ 
B)  $- \frac { 11 } { x ( x + 3 ) }$ 
C)  $\frac { 12 } { ( x + 3 ) ( x - 3 ) }$ 
D)  $\frac { 11 ( x + h + 3 ) } { ( x + 3 ) }$ 
A)  $\frac { 11 } { ( x + h + 3 ) ( x + 3 ) }$ 
B)  $- \frac { 11 } { x ( x + 3 ) }$ 
C)  $\frac { 12 } { ( x + 3 ) ( x - 3 ) }$ 
D)  $\frac { 11 ( x + h + 3 ) } { ( x + 3 ) }$

Question 7

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function.
-The reflection of the graph of y = f(x) across the y-axis

Accepted Answer

A)  (-2, -4) 
B)  (2, 4) 
C)  (-2, 4) 
D)  (2, -4) 
A)  (-2, -4) 
B)  (2, 4) 
C)  (-2, 4) 
D)  (2, -4)

Question 8

Write an equation for the line described. Write the equation in the form specified.
-parallel to $5 x + 2 y = 43$; through $( 5,15 )$; standard form

Accepted Answer

A)  $5 x + 2 y = 55$ 
B)  $5 x + 2 y = 43$ 
C)  $5 x - 2 y = 55$ 
D)  $2 x + 5 y = 15$ 
A)  $5 x + 2 y = 55$ 
B)  $5 x + 2 y = 43$ 
C)  $5 x - 2 y = 55$ 
D)  $2 x + 5 y = 15$

Question 9

Match the description with the correct symbolic expression.
-a horizontal line

Accepted Answer

A)  y = -9x + 9 
B) 9x + 9y = -6 
C)  f(x) = 9 
D)  x = -9 
A)  y = -9x + 9 
B) 9x + 9y = -6 
C)  f(x) = 9 
D)  x = -9

Question 10

For the given functions f and g , find the indicated composition.
-$$f ( x ) = 3 x + 10 , \quad g ( x ) = 4 x - 1$$
$( \mathrm { f } \circ \mathrm { g } ) ( \mathrm { x } )$

Accepted Answer

A)  $12 x + 7$ 
B)  $12 x + 39$ 
C)  $12 x + 13$ 
D)  $12 x + 9$ 
A)  $12 x + 7$ 
B)  $12 x + 39$ 
C)  $12 x + 13$ 
D)  $12 x + 9$

Question 11

Find the requested value.
-$f ( 7 )$ for $f ( x ) = \left\{ \begin{array} { l l } 2 x + 5 , & \text { if } x \leq 0 \ 4 - 6 x , & \text { if } 0 < x < 6 \ x , & \text { if } x \geq 6 \end{array} \right.$

Accepted Answer

A)  6 
B)  7 
C)  19 
D)  $- 38$ 
A)  6 
B)  7 
C)  19 
D)  $- 38$

Question 12

Find the center-radius form of the circle described or graphed.
-

Accepted Answer

A)  $( x + 4 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 3$ 
B)  $( x + 4 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 9$ 
C)  $( x - 4 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 9$ 
D)  $( x - 4 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 3$ 
A)  $( x + 4 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 3$ 
B)  $( x + 4 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 9$ 
C)  $( x - 4 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 9$ 
D)  $( x - 4 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 3$

Question 13

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

Accepted Answer

A) $f ( x ) = \left\{ \begin{array} { c l } - 5 & \text { if } x 4 \end{array} ; \right.$ Domain: $( - \infty - 3 ] \cup ( 4 , \infty )$, Range: $\{ - 5,4 \}$ C) $f ( x ) = \left\{ \begin{array} { c l } - 5 & \text { if } x \leq - 3 \ 4 & \text { if } x > 4 \end{array} ; \right.$ Domain: $\{ - 5,4 \}$, Range: $( - \infty - 3 ] \cup ( 4 , \infty )$ D) $f ( x ) = \left\{ \begin{array} { c l } - 5 & \text { if } x < - 3 \ 4 & \text { if } x \geq 4 \end{array} \right.$; Domain: $\{ - 5,4 \}$, Range: $( - \infty - 3 ) \cup [ 4 , \infty )$ A) $f ( x ) = \left\{ \begin{array} { c l } - 5 & \text { if } x 4 \end{array} ; \right.$ Domain: $( - \infty - 3 ] \cup ( 4 , \infty )$, Range: $\{ - 5,4 \}$ C) $f ( x ) = \left\{ \begin{array} { c l } - 5 & \text { if } x \leq - 3 \ 4 & \text { if } x > 4 \end{array} ; \right.$ Domain: $\{ - 5,4 \}$, Range: $( - \infty - 3 ] \cup ( 4 , \infty )$ D) $f ( x ) = \left\{ \begin{array} { c l } - 5 & \text { if } x < - 3 \ 4 & \text { if } x \geq 4 \end{array} \right.$; Domain: $\{ - 5,4 \}$, Range: $( - \infty - 3 ) \cup [ 4 , \infty )$

Question 14

Solve the problem.
-Find the center-radius form of the equation of the circle having a diameter with endpoints $( - 5,1 )$ and $( 3,7 )$.

Accepted Answer

A)  $( x + 3 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 10$ 
B)  $( x - 3 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 100$ 
C)  $( x - 1 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 5$ 
D)  $( x + 1 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 25$ 
A)  $( x + 3 ) ^ { 2 } + ( y - 7 ) ^ { 2 } = 10$ 
B)  $( x - 3 ) ^ { 2 } + ( y + 7 ) ^ { 2 } = 100$ 
C)  $( x - 1 ) ^ { 2 } + ( y + 4 ) ^ { 2 } = 5$ 
D)  $( x + 1 ) ^ { 2 } + ( y - 4 ) ^ { 2 } = 25$

Question 15

The graph of a linear function f is shown. Write the equation that defines f. Write the equation in slope -intercept form.
-

Accepted Answer

A)  $y = 5 x - 5$ 
B)  $y = - 5 x - 5$ 
C)  $y = - 5 x + 5$ 
D)  $y = 5 x + 5$ 
A)  $y = 5 x - 5$ 
B)  $y = - 5 x - 5$ 
C)  $y = - 5 x + 5$ 
D)  $y = 5 x + 5$

Question 16

Decide whether the relation defines a function.
-

Accepted Answer

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

Question 17

Solve the problem.
-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
24 has a rate of return of 25.0%. What is the average rate of change in return per unit of risk?
Round to two decimal places.

Accepted Answer

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

Question 18

Solve the problem. Write all linear equations in slope-intercept form.
-In a lab experiment 6 grams of acid were produced in 21 minutes and 18 grams in 31 minutes. Find a linear equation that models the number of grams produced in $x$ minutes.

Accepted Answer

A)  $y = \frac { 6 } { 5 } x + \frac { 96 } { 5 }$ 
B)  $y = \frac { 6 } { 5 } x - \frac { 96 } { 5 }$ 
C)  $y = x + 15$ 
D)  $y = \frac { 5 } { 6 } x - \frac { 5 } { 96 }$ 
A)  $y = \frac { 6 } { 5 } x + \frac { 96 } { 5 }$ 
B)  $y = \frac { 6 } { 5 } x - \frac { 96 } { 5 }$ 
C)  $y = x + 15$ 
D)  $y = \frac { 5 } { 6 } x - \frac { 5 } { 96 }$

Question 19

Determine whether the three points are collinear.
-(2, 11), (-2, 3), (10, 15)

Accepted Answer

A)  Yes 
B)  No 
A)  Yes 
B)  No

Question 20

Consider the function h as defined. Find functions f and g so that (f ∘ g)(x) = h(x).
-$$h ( x ) = ( - 6 x + 18 ) ^ { 2 }$$

Accepted Answer

A)  $f ( x ) = - 6 x + 18 , g ( x ) = x ^ { 2 }$ 
B)  $f ( x ) = x ^ { 2 } , g ( x ) = - 6 x + 18$ 
C)  $f ( x ) = ( - 6 x ) ^ { 2 } , g ( x ) = 18$ 
D)  $f ( x ) = - 6 x ^ { 2 } , g ( x ) = x + 18$ 
A)  $f ( x ) = - 6 x + 18 , g ( x ) = x ^ { 2 }$ 
B)  $f ( x ) = x ^ { 2 } , g ( x ) = - 6 x + 18$ 
C)  $f ( x ) = ( - 6 x ) ^ { 2 } , g ( x ) = 18$ 
D)  $f ( x ) = - 6 x ^ { 2 } , g ( x ) = x + 18$

Decide whether the relation defines a function. -

Solve the problem. -Use the graphs to find the value of $\left( \frac { f } { g } \right) ( 3 )$ . $Solve the problem. -Use the graphs to find the value of \left( \frac { f } { g } \right) ( 3 ) .$

Graph the function. - $f(x)=(7 x)^{2}$ $Graph the function. - f(x)=(7 x)^{2}$

Determine whether (f ∘ g)(x) = x and whether (g ∘ f)(x) = x. - $f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 }$

Compute and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$ - $f ( x ) = \frac { x - 8 } { x + 3 }$

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. -The reflection of the graph of y = f(x) across the y-axis

Write an equation for the line described. Write the equation in the form specified. -parallel to $5 x + 2 y = 43$ ; through $( 5,15 )$ ; standard form

Match the description with the correct symbolic expression. -a horizontal line

For the given functions f and g , find the indicated composition. - $f ( x ) = 3 x + 10 , \quad g ( x ) = 4 x - 1$ $( \mathrm { f } \circ \mathrm { g } ) ( \mathrm { x } )$

Find the requested value. - $f ( 7 )$ for $f ( x ) = \left\{ \begin{array} { l l } 2 x + 5 , & \text { if } x \leq 0 \\ 4 - 6 x , & \text { if } 0 < x < 6 \\ x , & \text { if } x \geq 6 \end{array} \right.$

Find the center-radius form of the circle described or graphed. -

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

Solve the problem. -Find the center-radius form of the equation of the circle having a diameter with endpoints $( - 5,1 )$ and $( 3,7 )$ .

The graph of a linear function f is shown. Write the equation that defines f. Write the equation in slope -intercept form. -

Decide whether the relation defines a function. -

Solve the problem. Write all linear equations in slope-intercept form. -In a lab experiment 6 grams of acid were produced in 21 minutes and 18 grams in 31 minutes. Find a linear equation that models the number of grams produced in $x$ minutes.

Determine whether the three points are collinear. -(2, 11), (-2, 3), (10, 15)

Consider the function h as defined. Find functions f and g so that (f ∘ g)(x) = h(x). - $h ( x ) = ( - 6 x + 18 ) ^ { 2 }$

Equations and Inequalities

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 2: Graphs and Functions

Decide whether the relation defines a function. -

Solve the problem. -Use the graphs to find the value of (fg)(3)\left( \frac { f } { g } \right) ( 3 )(gf​)(3) .

Graph the function. - f(x)=(7x)2f(x)=(7 x)^{2}f(x)=(7x)2

Determine whether (f ∘ g)(x) = x and whether (g ∘ f)(x) = x. - f(x)=x+1,g(x)=x2f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 }f(x)=x+1​,g(x)=x2

Compute and simplify the difference quotient f(x+h)−f(x)h,h≠0\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0hf(x+h)−f(x)​,h=0 - f(x)=x−8x+3f ( x ) = \frac { x - 8 } { x + 3 }f(x)=x+3x−8​

Suppose the point (2, 4) is on the graph of y = f(x). Find a point on the graph of the given function. -The reflection of the graph of y = f(x) across the y-axis

Write an equation for the line described. Write the equation in the form specified. -parallel to 5x+2y=435 x + 2 y = 435x+2y=43 ; through (5,15)( 5,15 )(5,15) ; standard form

Match the description with the correct symbolic expression. -a horizontal line

For the given functions f and g , find the indicated composition. - f(x)=3x+10,g(x)=4x−1f ( x ) = 3 x + 10 , \quad g ( x ) = 4 x - 1f(x)=3x+10,g(x)=4x−1 (f∘g)(x)( \mathrm { f } \circ \mathrm { g } ) ( \mathrm { x } )(f∘g)(x)

Find the center-radius form of the circle described or graphed. -

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

Solve the problem. -Find the center-radius form of the equation of the circle having a diameter with endpoints (−5,1)( - 5,1 )(−5,1) and (3,7)( 3,7 )(3,7) .

The graph of a linear function f is shown. Write the equation that defines f. Write the equation in slope -intercept form. -

Decide whether the relation defines a function. -

Solve the problem. Write all linear equations in slope-intercept form. -In a lab experiment 6 grams of acid were produced in 21 minutes and 18 grams in 31 minutes. Find a linear equation that models the number of grams produced in xxx minutes.

Determine whether the three points are collinear. -(2, 11), (-2, 3), (10, 15)

Consider the function h as defined. Find functions f and g so that (f ∘ g)(x) = h(x). - h(x)=(−6x+18)2h ( x ) = ( - 6 x + 18 ) ^ { 2 }h(x)=(−6x+18)2

Equations and Inequalities

Polynomial and Rational Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Solve the problem. -Use the graphs to find the value of $\left( \frac { f } { g } \right) ( 3 )$ . $Solve the problem. -Use the graphs to find the value of \left( \frac { f } { g } \right) ( 3 ) .$

Graph the function. - $f(x)=(7 x)^{2}$ $Graph the function. - f(x)=(7 x)^{2}$

Determine whether (f ∘ g)(x) = x and whether (g ∘ f)(x) = x. - $f ( x ) = \sqrt { x + 1 } , g ( x ) = x ^ { 2 }$

Compute and simplify the difference quotient $\frac { f ( x + h ) - f ( x ) } { h } , h \neq 0$ - $f ( x ) = \frac { x - 8 } { x + 3 }$

Write an equation for the line described. Write the equation in the form specified. -parallel to $5 x + 2 y = 43$ ; through $( 5,15 )$ ; standard form

For the given functions f and g , find the indicated composition. - $f ( x ) = 3 x + 10 , \quad g ( x ) = 4 x - 1$ $( \mathrm { f } \circ \mathrm { g } ) ( \mathrm { x } )$

Solve the problem. -Find the center-radius form of the equation of the circle having a diameter with endpoints $( - 5,1 )$ and $( 3,7 )$ .

Solve the problem. Write all linear equations in slope-intercept form. -In a lab experiment 6 grams of acid were produced in 21 minutes and 18 grams in 31 minutes. Find a linear equation that models the number of grams produced in $x$ minutes.

Consider the function h as defined. Find functions f and g so that (f ∘ g)(x) = h(x). - $h ( x ) = ( - 6 x + 18 ) ^ { 2 }$