Question 1

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph.
-$$x ^ { 2 } + y ^ { 2 } + 8 x - 8 y + 32 = 0$$

Accepted Answer

A)  no; the graph is the point $( 4 , - 4 )$ 
B)  no; the graph is nonexistent 
C)  yes 
D)  no; the graph is the point $( - 4,4 )$ 
A)  no; the graph is the point $( 4 , - 4 )$ 
B)  no; the graph is nonexistent 
C)  yes 
D)  no; the graph is the point $( - 4,4 )$

Question 2

Find the slope of the line and sketch the graph.
-$y=6 x-1$

Accepted Answer

A)  $\mathrm { m } = - 6$
  
B)  $\mathrm { m } = \frac { 1 } { 6 }$
  
C)  $m = - 1$
  
D)  $m = 6$
  
A)  $\mathrm { m } = - 6$
  
B)  $\mathrm { m } = \frac { 1 } { 6 }$
  
C)  $m = - 1$
  
D)  $m = 6$

Question 3

Find the center-radius form of the equation of the circle.
-center $( - 1,3 )$, radius 6

Accepted Answer

A)  $( x - 1 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 36$ 
B)  $( x - 3 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 6$ 
C)  $( x + 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 6$ 
D)  $( x + 1 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 36$ 
A)  $( x - 1 ) ^ { 2 } + ( y + 3 ) ^ { 2 } = 36$ 
B)  $( x - 3 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 6$ 
C)  $( x + 3 ) ^ { 2 } + ( y - 1 ) ^ { 2 } = 6$ 
D)  $( x + 1 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 36$

Question 4

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph.
-$$x ^ { 2 } + y ^ { 2 } - 4 x - 2 y - 59 = 0$$

Accepted Answer

A)  no; the graph is the point $( 2,1 )$ 
B)  yes 
C)  no; the graph is nonexistent 
D)  no; the graph is the point $( - 2 , - 1 )$ 
A)  no; the graph is the point $( 2,1 )$ 
B)  yes 
C)  no; the graph is nonexistent 
D)  no; the graph is the point $( - 2 , - 1 )$

Question 5

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such.
-$6 x-12 y=12$

Accepted Answer

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

Question 6

Provide an appropriate response.
-If a horizontal line is drawn through the point $( 7,8 )$, where will it intersect the $y$-axis?

Accepted Answer

A)  $( 8,0 )$ 
B)  $( 0,8 )$ 
C)  $( 7,0 )$ 
D)  $( 0,7 )$ 
A)  $( 8,0 )$ 
B)  $( 0,8 )$ 
C)  $( 7,0 )$ 
D)  $( 0,7 )$

Question 7

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

Accepted Answer

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

Question 8

Find the requested value.
-Using the given tables, find $( \mathrm { f } \cdot \mathrm { g } ) ( 3 )$

Accepted Answer

A)  5 
B)  10 
C)  14 
D)  3 
A)  5 
B)  10 
C)  14 
D)  3

Question 9

Solve the problem.
-Suppose that receiving stations $X , Y$, and $Z$ are located on a coordinate plane at the points $( - 2,2 )$, $( - 14,10 )$, and $( - 10 , - 14 )$ 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 $( - 6,0 )$ 
B)  at $( - 4 , - 3 )$ 
C)  at $( - 4 , - 2 )$ 
D)  at $( - 5 , - 2 )$ 
A)  at $( - 6,0 )$ 
B)  at $( - 4 , - 3 )$ 
C)  at $( - 4 , - 2 )$ 
D)  at $( - 5 , - 2 )$

Question 10

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such.
-$h(x)=-5 x$

Accepted Answer

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

Question 11

Find the slope of the line and sketch the graph.
-$y+2=0$

Accepted Answer

A)  m: undefined
  
B)  $\mathrm { m } = 0$
  
C)  $m = - 2$
  
D)  $\mathrm { m } = - \frac { 1 } { 2 }$
  
A)  m: undefined
  
B)  $\mathrm { m } = 0$
  
C)  $m = - 2$
  
D)  $\mathrm { m } = - \frac { 1 } { 2 }$

Question 12

For the given functions f and g , find the indicated composition.
-$$f ( x ) = \frac { 3 } { x + 6 } , \quad g ( x ) = \frac { 5 } { 6 x }$$
$( f \circ g ) ( x )$

Accepted Answer

A)  $\frac { 18 x } { 5 - 36 x }$ 
B)  $\frac { 3 x } { 5 + 36 x }$ 
C)  $\frac { 18 x } { 5 + 36 x }$ 
D)  $\frac { 5 x + 30 } { 18 x }$ 
A)  $\frac { 18 x } { 5 - 36 x }$ 
B)  $\frac { 3 x } { 5 + 36 x }$ 
C)  $\frac { 18 x } { 5 + 36 x }$ 
D)  $\frac { 5 x + 30 } { 18 x }$

Question 13

Find the specified domain.
-Find the domain of $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } )$ when $\mathrm { f } ( \mathrm { x } ) = \frac { 5 } { \mathrm { x } - 3 }$ and $\mathrm { g } ( \mathrm { x } ) = 6 - \mathrm { x }$

Accepted Answer

A)  $( - \infty , 3 ) \cup ( 3 , \infty )$ 
B)  $( - \infty , 6 ) \cup ( 6 , \infty )$ 
C)  $( - \infty , 3 ) \cup ( 3,6 ) \cup ( 6 , \infty )$ 
D)  $( - \infty , - 6 ) \cup ( - 6 , - 3 ) \cup ( - 3 , \infty )$ 
A)  $( - \infty , 3 ) \cup ( 3 , \infty )$ 
B)  $( - \infty , 6 ) \cup ( 6 , \infty )$ 
C)  $( - \infty , 3 ) \cup ( 3,6 ) \cup ( 6 , \infty )$ 
D)  $( - \infty , - 6 ) \cup ( - 6 , - 3 ) \cup ( - 3 , \infty )$

Question 14

Match the equation with the correct graph.
-$$x = 2$$

Accepted Answer

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

Question 15

Write an equation for the line described. Write the equation in the form specified.
-perpendicular to $7 x - 6 y = 2$, through $( 8 , - 9 )$; standard form

Accepted Answer

A)  $6 x - 7 y = - 15$ 
B)  $8 x + 6 y = 2$ 
C)  $6 x + 7 y = - 15$ 
D)  $7 x + 6 = 7$ 
A)  $6 x - 7 y = - 15$ 
B)  $8 x + 6 y = 2$ 
C)  $6 x + 7 y = - 15$ 
D)  $7 x + 6 = 7$

Question 16

Find the specified domain.
-Find the domain of $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } )$ when $\mathrm { f } ( \mathrm { x } ) = 2 \mathrm { x } - 5$ and $g ( x ) = \frac { 2 } { \mathrm { x } - 7 }$

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $\left( - \infty , \frac { 5 } { 2 } \right) \cup \left( \frac { 5 } { 2 } , 7 \right) \cup ( 7 , \infty )$ 
C)  $( - \infty , 7 ) \cup ( 7 , \infty )$ 
D)  $( - \infty , - 7 ) \cup ( - 7 , \infty )$ 
A)  $( - \infty , \infty )$ 
B)  $\left( - \infty , \frac { 5 } { 2 } \right) \cup \left( \frac { 5 } { 2 } , 7 \right) \cup ( 7 , \infty )$ 
C)  $( - \infty , 7 ) \cup ( 7 , \infty )$ 
D)  $( - \infty , - 7 ) \cup ( - 7 , \infty )$

Question 17

Solve the problem.
-Find all values of $y$ such that the distance between $( 2 , y )$ and $( - 10,3 )$ is 13 .

Accepted Answer

A)  $- 8,2$ 
B)  2,8 
C)  $- 8 , - 2$ 
D)  $- 2,8$ 
A)  $- 8,2$ 
B)  2,8 
C)  $- 8 , - 2$ 
D)  $- 2,8$

Question 18

Give the domain and range of the relation.
-

Accepted Answer

A)  domain: $[ - 1,3 ]$; range: $[ - 3,0 ]$ 
B)  domain: $( - \infty , 3 ]$; range: $[ 0,3 ]$ 
C) $\text { domain: }[-3,0] \text {; range: }[-1,3]$ 
D)  domain: $[ 0,3 ]$; range: $( - \infty , 3 ]$ 
A)  domain: $[ - 1,3 ]$; range: $[ - 3,0 ]$ 
B)  domain: $( - \infty , 3 ]$; range: $[ 0,3 ]$ 
C) $\text { domain: }[-3,0] \text {; range: }[-1,3]$ 
D)  domain: $[ 0,3 ]$; range: $( - \infty , 3 ]$

Question 19

Write an equation for the line described. Write the equation in the form specified.
-parallel to $- 5 x + 7 y = 54$, through $( - 8,0 )$; slope-intercept form

Accepted Answer

A)  $y = \frac { 8 } { 7 } x + \frac { 54 } { 7 }$ 
B)  $\mathrm { y } = \frac { 5 } { 7 } \mathrm { x } + \frac { 40 } { 7 }$ 
C)  $y = \frac { 7 } { 5 } x + 0$ 
D)  $y = - \frac { 5 } { 7 } x - \frac { 40 } { 7 }$ 
A)  $y = \frac { 8 } { 7 } x + \frac { 54 } { 7 }$ 
B)  $\mathrm { y } = \frac { 5 } { 7 } \mathrm { x } + \frac { 40 } { 7 }$ 
C)  $y = \frac { 7 } { 5 } x + 0$ 
D)  $y = - \frac { 5 } { 7 } x - \frac { 40 } { 7 }$

Question 20

Determine the intervals of the domain for which the function is increasing, decreasing, and constant.
-

Accepted Answer

A) $\text { Increasing }(-\infty, 0] \text {; Decreasing }[0,-\infty)$ 
B)  Increasing $( - \infty , 0 ]$; Decreasing $( - \infty , 0 ]$ 
C)  Increasing $[ 0 , \infty )$; Decreasing $( - \infty , 0 ]$ 
D)  Increasing $( - \infty , 0 ]$; Decreasing $[ 0 , \infty )$ 
A) $\text { Increasing }(-\infty, 0] \text {; Decreasing }[0,-\infty)$ 
B)  Increasing $( - \infty , 0 ]$; Decreasing $( - \infty , 0 ]$ 
C)  Increasing $[ 0 , \infty )$; Decreasing $( - \infty , 0 ]$ 
D)  Increasing $( - \infty , 0 ]$; Decreasing $[ 0 , \infty )$

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - $x ^ { 2 } + y ^ { 2 } + 8 x - 8 y + 32 = 0$

Find the slope of the line and sketch the graph. - $y=6 x-1$

Find the center-radius form of the equation of the circle. -center $( - 1,3 )$ , radius 6

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - $x ^ { 2 } + y ^ { 2 } - 4 x - 2 y - 59 = 0$

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. - $6 x-12 y=12$

Provide an appropriate response. -If a horizontal line is drawn through the point $( 7,8 )$ , where will it intersect the $y$ -axis?

Find the requested value. -Using the given tables, find $( \mathrm { f } \cdot \mathrm { g } ) ( 3 )$

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. - $h(x)=-5 x$

Find the slope of the line and sketch the graph. - $y+2=0$

For the given functions f and g , find the indicated composition. - $f ( x ) = \frac { 3 } { x + 6 } , \quad g ( x ) = \frac { 5 } { 6 x }$ $( f \circ g ) ( x )$

Find the specified domain. -Find the domain of $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } )$ when $\mathrm { f } ( \mathrm { x } ) = \frac { 5 } { \mathrm { x } - 3 }$ and $\mathrm { g } ( \mathrm { x } ) = 6 - \mathrm { x }$

Match the equation with the correct graph. - $x = 2$

Write an equation for the line described. Write the equation in the form specified. -perpendicular to $7 x - 6 y = 2$ , through $( 8 , - 9 )$ ; standard form

Find the specified domain. -Find the domain of $\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } )$ when $\mathrm { f } ( \mathrm { x } ) = 2 \mathrm { x } - 5$ and $g ( x ) = \frac { 2 } { \mathrm { x } - 7 }$

Solve the problem. -Find all values of $y$ such that the distance between $( 2 , y )$ and $( - 10,3 )$ is 13 .

Give the domain and range of the relation. -

Write an equation for the line described. Write the equation in the form specified. -parallel to $- 5 x + 7 y = 54$ , through $( - 8,0 )$ ; slope-intercept form

Determine the intervals of the domain for which the function is increasing, decreasing, and constant. -

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

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Exam 2: Graphs and Functions

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - x2+y2+8x−8y+32=0x ^ { 2 } + y ^ { 2 } + 8 x - 8 y + 32 = 0x2+y2+8x−8y+32=0

Find the slope of the line and sketch the graph. - y=6x−1y=6 x-1y=6x−1

Find the center-radius form of the equation of the circle. -center (−1,3)( - 1,3 )(−1,3) , radius 6

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - x2+y2−4x−2y−59=0x ^ { 2 } + y ^ { 2 } - 4 x - 2 y - 59 = 0x2+y2−4x−2y−59=0

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. - 6x−12y=126 x-12 y=126x−12y=12

Provide an appropriate response. -If a horizontal line is drawn through the point (7,8)( 7,8 )(7,8) , where will it intersect the yyy -axis?

The figure below shows the graph of a function y = f(x). Use this graph to solve the problem. - 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).

Find the requested value. -Using the given tables, find (f⋅g)(3)( \mathrm { f } \cdot \mathrm { g } ) ( 3 )(f⋅g)(3)

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. - h(x)=−5xh(x)=-5 xh(x)=−5x

Find the slope of the line and sketch the graph. - y+2=0y+2=0y+2=0

For the given functions f and g , find the indicated composition. - f(x)=3x+6,g(x)=56xf ( x ) = \frac { 3 } { x + 6 } , \quad g ( x ) = \frac { 5 } { 6 x }f(x)=x+63​,g(x)=6x5​ (f∘g)(x)( f \circ g ) ( x )(f∘g)(x)

Match the equation with the correct graph. - x=2x = 2x=2

Write an equation for the line described. Write the equation in the form specified. -perpendicular to 7x−6y=27 x - 6 y = 27x−6y=2 , through (8,−9)( 8 , - 9 )(8,−9) ; standard form

Find the specified domain. -Find the domain of (fg)(x)\left( \frac { \mathrm { f } } { \mathrm { g } } \right) ( \mathrm { x } )(gf​)(x) when f(x)=2x−5\mathrm { f } ( \mathrm { x } ) = 2 \mathrm { x } - 5f(x)=2x−5 and g(x)=2x−7g ( x ) = \frac { 2 } { \mathrm { x } - 7 }g(x)=x−72​

Solve the problem. -Find all values of yyy such that the distance between (2,y)( 2 , y )(2,y) and (−10,3)( - 10,3 )(−10,3) is 13 .