Question 1

Solve the problem.
- 
The graphs of functions $f$ and $g$ are shown. Use these graphs to find $( f + g ) ( - 4 )$.

Accepted Answer

A)  $- \frac { 1 } { 4 }$ 
B)  $- 5$ 
C)  $- 4$ 
D)  3 
A)  $- \frac { 1 } { 4 }$ 
B)  $- 5$ 
C)  $- 4$ 
D)  3

Question 2

Find the center-radius form of the equation of the circle.
-center $( - \sqrt { 3 } , - 9 )$, radius $\sqrt { 3 }$

Accepted Answer

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

Question 3

Evaluate the function.
-Find $f ( 3 )$ when $f ( x ) = 2 x ^ { 2 } - 3 x + 3$

Accepted Answer

A)  6 
B)  30 
C)  12 
D)  3 
A)  6 
B)  30 
C)  12 
D)  3

Question 4

Use a graphing calculator to solve the linear equation.
-$$- 8 x + 3 + 6 x = - 2 x + 8$$

Accepted Answer

A)  $\{ 5 \}$ 
B)  $\{ - 3 \}$ 
C)  all real numbers 
D)  $\varnothing$ 
A)  $\{ 5 \}$ 
B)  $\{ - 3 \}$ 
C)  all real numbers 
D)  $\varnothing$

Question 5

Give the domain and range of the relation.
-$$y = \sqrt { 2 x - 7 }$$

Accepted Answer

A)  domain: $\left[ \frac { 7 } { 2 } , \infty \right)$; range: $( - \infty , \infty )$ 
B)  domain: $\left( \frac { 7 } { 2 } , \infty \right)$; range: $[ 0 , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $\left[ \frac { 7 } { 2 } , \infty \right)$ 
D)  domain: $\left[ \frac { 7 } { 2 } , \infty \right\}$; range: $[ 0 , \infty )$ 
A)  domain: $\left[ \frac { 7 } { 2 } , \infty \right)$; range: $( - \infty , \infty )$ 
B)  domain: $\left( \frac { 7 } { 2 } , \infty \right)$; range: $[ 0 , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $\left[ \frac { 7 } { 2 } , \infty \right)$ 
D)  domain: $\left[ \frac { 7 } { 2 } , \infty \right\}$; range: $[ 0 , \infty )$

Question 6

Find the specified domain.
-Find the domain of $( f + g ) ( x )$ when $f ( x ) = \sqrt { 6 x - 2 }$ and $g ( x ) = \frac { 1 } { x }$

Accepted Answer

A)  $\left[ - \frac { 1 } { 3 } , \infty \right)$ 
B)  $\left[ \frac { 1 } { 3 } , \infty \right]$ 
C)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
D)  $\left[ - \frac { 1 } { 3 } , 0 \right] \cup ( 0 , \infty )$ 
A)  $\left[ - \frac { 1 } { 3 } , \infty \right)$ 
B)  $\left[ \frac { 1 } { 3 } , \infty \right]$ 
C)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
D)  $\left[ - \frac { 1 } { 3 } , 0 \right] \cup ( 0 , \infty )$

Question 7

Provide an appropriate response.
-What is the midpoint of the segment joining $( a , z )$ and $( - 5 a , 7 z )$ ?

Accepted Answer

A)  $( - 2 a , 4 z )$ 
B)  $( - 4 a , 8 z )$ 
C)  $( 2 a , 3 z )$ 
D)  $( - 3 a , 4 z )$ 
A)  $( - 2 a , 4 z )$ 
B)  $( - 4 a , 8 z )$ 
C)  $( 2 a , 3 z )$ 
D)  $( - 3 a , 4 z )$

Question 8

Find the requested value.
-Using the given tables, find $( g \circ g ) ( 2 )$

Accepted Answer

A)  5 
B)  9 
C)  7 
D)  3 
A)  5 
B)  9 
C)  7 
D)  3

Question 9

Determine whether the equation has a graph that is symmetric with respect to the y -axis, the x-axis, the origin, or none
of these.
-$$y = 4 x ^ { 2 } + 5$$

Accepted Answer

A)  $y$-axis only 
B)  $x$-axis only 
C)  $x$-axis, $y$-axis, origin 
D)  origin only 
A)  $y$-axis only 
B)  $x$-axis only 
C)  $x$-axis, $y$-axis, origin 
D)  origin only

Question 10

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

Accepted Answer

A)  (2, 6) 
B)  (0, 4) 
C)  (2, 2) 
D)  (4, 4) 
A)  (2, 6) 
B)  (0, 4) 
C)  (2, 2) 
D)  (4, 4)

Question 11

For the points P and Q, find the distance d(P, Q).
-$\mathrm { P } ( 3 , - 6 ) , \mathrm { Q } ( 7 , - 4 )$

Accepted Answer

A)  12 
B)  $2 \sqrt { 5 }$ 
C)  2 
D)  $12 \sqrt { 3 }$ 
A)  12 
B)  $2 \sqrt { 5 }$ 
C)  2 
D)  $12 \sqrt { 3 }$

Question 12

Describe the transformations and give the equation for the graph.
-

Accepted Answer

A)  It is the graph of $f ( x ) = \sqrt { x }$ translated 3 units to the left and translated 5 units up. The equation is $y = \sqrt { x + 3 } - 5$ 
B)  It is the graph of $f ( x ) = \sqrt { x }$ translated 3 units to the left and translated 5 units up. The equation is $y = \sqrt { x + 3 } + 5$ 
C)  It is the graph of $f ( x ) = \sqrt { x }$ translated 3 units to the left and translated 5 units up. The equation is $y = \sqrt { x - 3 } - 5$ 
D)  It is the graph of $f ( x ) = \sqrt { x }$ translated 3 units to the left and translated 5 units up. The equation is $y = \sqrt { x - 3 } + 5$ 
A)  It is the graph of $f ( x ) = \sqrt { x }$ translated 3 units to the left and translated 5 units up. The equation is $y = \sqrt { x + 3 } - 5$ 
B)  It is the graph of $f ( x ) = \sqrt { x }$ translated 3 units to the left and translated 5 units up. The equation is $y = \sqrt { x + 3 } + 5$ 
C)  It is the graph of $f ( x ) = \sqrt { x }$ translated 3 units to the left and translated 5 units up. The equation is $y = \sqrt { x - 3 } - 5$ 
D)  It is the graph of $f ( x ) = \sqrt { x }$ translated 3 units to the left and translated 5 units up. The equation is $y = \sqrt { x - 3 } + 5$

Question 13

Graph the point symmetric to the given point.
-Plot the point (3, 2), then plot the point that is symmetric to (3, 2) with respect to the y-axis.

Accepted Answer

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

Question 14

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

Accepted Answer

A)  x = 9 
B)  f(x) = -9x + 9 
C) y = 9x + 2 
D) 9x - 4y = 2 
A)  x = 9 
B)  f(x) = -9x + 9 
C) y = 9x + 2 
D) 9x - 4y = 2

Question 15

Find the center-radius form of the circle described or graphed.
-a circle having a diameter with endpoints $( - 4,0 )$ and $( 6 , - 6 )$

Accepted Answer

A)  $( x + 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 34$ 
B)  $( x - 1 ) ^ { 2 } + y ^ { 2 } = 9$ 
C)  $( x - 1 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 34$ 
D)  $x ^ { 2 } + ( y + 3 ) ^ { 2 } = 25$ 
A)  $( x + 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 34$ 
B)  $( x - 1 ) ^ { 2 } + y ^ { 2 } = 9$ 
C)  $( x - 1 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 34$ 
D)  $x ^ { 2 } + ( y + 3 ) ^ { 2 } = 25$

Question 16

Evaluate.
-Find $( f g ) ( - 4 )$ when $f ( x ) = x + 3$ and $g ( x ) = 4 x ^ { 2 } + 12 x + 2$

Accepted Answer

A)  30 
B)  $- 18$ 
C)  $- 126$ 
D)  $- 462$ 
A)  30 
B)  $- 18$ 
C)  $- 126$ 
D)  $- 462$

Question 17

For the pair of functions, find the indicated sum, difference, product, or quotient.
-$$f ( x ) = 7 - 7 x , g ( x ) = - 4 x + 7$$
Find $( f + g ) ( x )$

Accepted Answer

A)  $- 3 x + 14$ 
B)  $- 11 x + 14$ 
C)  $- 4 x + 7$ 
D)  $3 x$ 
A)  $- 3 x + 14$ 
B)  $- 11 x + 14$ 
C)  $- 4 x + 7$ 
D)  $3 x$

Question 18

Graph the line and give the domain and the range.
-$$4 y + 36 = 0$$

Accepted Answer

A)  $\mathrm { D } = \{ - 9 \} , \mathrm { R } = ( - \infty , \infty )$
  
B)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = \{ - 9 \}$
  
C)  $D = ( - \infty , \infty ) , R = \{ - 9 \}$
  
D)  $\mathrm { D } = \{ - 9 \} , \mathrm { R } = ( - \infty , \infty )$
  
A)  $\mathrm { D } = \{ - 9 \} , \mathrm { R } = ( - \infty , \infty )$
  
B)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = \{ - 9 \}$
  
C)  $D = ( - \infty , \infty ) , R = \{ - 9 \}$
  
D)  $\mathrm { D } = \{ - 9 \} , \mathrm { R } = ( - \infty , \infty )$

Question 19

Determine whether the equation has a graph that is symmetric with respect to the y -axis, the x-axis, the origin, or none
of these.
-$$y = - 7 x ^ { 3 } + 9 x$$

Accepted Answer

A)  $x$-axis only 
B)  $\mathrm { y }$-axis only 
C)  origin only 
D)  $x$-axis, $y$-axis, origin 
A)  $x$-axis only 
B)  $\mathrm { y }$-axis only 
C)  origin only 
D)  $x$-axis, $y$-axis, origin

Question 20

Determine whether the equation has a graph that is symmetric with respect to the y -axis, the x-axis, the origin, or none
of these.
-$$y = 0.58 x ^ { 4 } + x ^ { 2 } - 4$$

Accepted Answer

A)  $\mathrm { y }$-axis only 
B)  $x$-axis only 
C)  origin only 
D)  none of these 
A)  $\mathrm { y }$-axis only 
B)  $x$-axis only 
C)  origin only 
D)  none of these

Solve the problem. - The graphs of functions $f$ and $g$ are shown. Use these graphs to find $( f + g ) ( - 4 )$ .

Find the center-radius form of the equation of the circle. -center $( - \sqrt { 3 } , - 9 )$ , radius $\sqrt { 3 }$

Evaluate the function. -Find $f ( 3 )$ when $f ( x ) = 2 x ^ { 2 } - 3 x + 3$

Use a graphing calculator to solve the linear equation. - $- 8 x + 3 + 6 x = - 2 x + 8$

Give the domain and range of the relation. - $y = \sqrt { 2 x - 7 }$

Find the specified domain. -Find the domain of $( f + g ) ( x )$ when $f ( x ) = \sqrt { 6 x - 2 }$ and $g ( x ) = \frac { 1 } { x }$

Provide an appropriate response. -What is the midpoint of the segment joining $( a , z )$ and $( - 5 a , 7 z )$ ?

Find the requested value. -Using the given tables, find $( g \circ g ) ( 2 )$ $Find the requested value. -Using the given tables, find ( g \circ g ) ( 2 )$

Determine whether the equation has a graph that is symmetric with respect to the y -axis, the x-axis, the origin, or none of these. - $y = 4 x ^ { 2 } + 5$

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

For the points P and Q, find the distance d(P, Q). - $\mathrm { P } ( 3 , - 6 ) , \mathrm { Q } ( 7 , - 4 )$

Describe the transformations and give the equation for the graph. -

Graph the point symmetric to the given point. -Plot the point (3, 2), then plot the point that is symmetric to (3, 2) with respect to the y-axis.

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

Find the center-radius form of the circle described or graphed. -a circle having a diameter with endpoints $( - 4,0 )$ and $( 6 , - 6 )$

Evaluate. -Find $( f g ) ( - 4 )$ when $f ( x ) = x + 3$ and $g ( x ) = 4 x ^ { 2 } + 12 x + 2$

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = 7 - 7 x , g ( x ) = - 4 x + 7$ Find $( f + g ) ( x )$

Graph the line and give the domain and the range. - $4 y + 36 = 0$

Determine whether the equation has a graph that is symmetric with respect to the y -axis, the x-axis, the origin, or none of these. - $y = - 7 x ^ { 3 } + 9 x$

Determine whether the equation has a graph that is symmetric with respect to the y -axis, the x-axis, the origin, or none of these. - $y = 0.58 x ^ { 4 } + x ^ { 2 } - 4$

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

Solve the problem. - The graphs of functions fff and ggg are shown. Use these graphs to find (f+g)(−4)( f + g ) ( - 4 )(f+g)(−4) .

Find the center-radius form of the equation of the circle. -center (−3,−9)( - \sqrt { 3 } , - 9 )(−3​,−9) , radius 3\sqrt { 3 }3​

Evaluate the function. -Find f(3)f ( 3 )f(3) when f(x)=2x2−3x+3f ( x ) = 2 x ^ { 2 } - 3 x + 3f(x)=2x2−3x+3

Use a graphing calculator to solve the linear equation. - −8x+3+6x=−2x+8- 8 x + 3 + 6 x = - 2 x + 8−8x+3+6x=−2x+8

Give the domain and range of the relation. - y=2x−7y = \sqrt { 2 x - 7 }y=2x−7​

Find the specified domain. -Find the domain of (f+g)(x)( f + g ) ( x )(f+g)(x) when f(x)=6x−2f ( x ) = \sqrt { 6 x - 2 }f(x)=6x−2​ and g(x)=1xg ( x ) = \frac { 1 } { x }g(x)=x1​

Provide an appropriate response. -What is the midpoint of the segment joining (a,z)( a , z )(a,z) and (−5a,7z)( - 5 a , 7 z )(−5a,7z) ?

Find the requested value. -Using the given tables, find (g∘g)(2)( g \circ g ) ( 2 )(g∘g)(2)

Determine whether the equation has a graph that is symmetric with respect to the y -axis, the x-axis, the origin, or none of these. - y=4x2+5y = 4 x ^ { 2 } + 5y=4x2+5