Question 1

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph.
-$$x ^ { 2 } + y ^ { 2 } - 6 x + 8 y + 25 = 0$$

Accepted Answer

A)  no; the graph is nonexistent 
B)  yes 
C)  no; the graph is the point $( 3 , - 4 )$ 
D)  no; the graph is the point $( - 3,4 )$ 
A)  no; the graph is nonexistent 
B)  yes 
C)  no; the graph is the point $( 3 , - 4 )$ 
D)  no; the graph is the point $( - 3,4 )$

Question 2

Give the domain and range of the relation.
-

Accepted Answer

A)  range: $( - \infty , 4 ) \cup ( 4 , \infty )$; domain: $( - \infty , - 5 ) \cup ( - 5 , \infty )$ 
B)  range: $( - \infty , \infty )$; domain: $( - \infty , \infty )$ 
C)  range: $( - \infty , 0 ) \cup ( 0,4 ) \cup ( 4 , \infty )$; domain: $( - \infty , - 5 ) \cup ( - 5,0 ) \cup ( 0 , \infty )$ 
D)  None of these 
A)  range: $( - \infty , 4 ) \cup ( 4 , \infty )$; domain: $( - \infty , - 5 ) \cup ( - 5 , \infty )$ 
B)  range: $( - \infty , \infty )$; domain: $( - \infty , \infty )$ 
C)  range: $( - \infty , 0 ) \cup ( 0,4 ) \cup ( 4 , \infty )$; domain: $( - \infty , - 5 ) \cup ( - 5,0 ) \cup ( 0 , \infty )$ 
D)  None of these

Question 3

For the points P and Q, find the coordinates of the midpoint of the segment PQ.
-$$\mathrm { P } ( 11 \sqrt { 5 } , - \sqrt { 10 } ) , \mathrm { Q } ( - \sqrt { 5 } , 0 )$$

Accepted Answer

A)  $\left( 5 \sqrt { 5 } , - \frac { \sqrt { 10 } } { 2 } \right)$ 
B)  $\left( 5 \sqrt { 10 } , - \frac { \sqrt { 30 } } { 2 } \right)$ 
C)  $\left[ 6 \sqrt { 5 } , \frac { \sqrt { 10 } } { 2 } \right)$ 
D)  $( - 5,10 )$ 
A)  $\left( 5 \sqrt { 5 } , - \frac { \sqrt { 10 } } { 2 } \right)$ 
B)  $\left( 5 \sqrt { 10 } , - \frac { \sqrt { 30 } } { 2 } \right)$ 
C)  $\left[ 6 \sqrt { 5 } , \frac { \sqrt { 10 } } { 2 } \right)$ 
D)  $( - 5,10 )$

Question 4

Determine whether the three points are collinear.
-(5, 11), (-3, 6), (10, 19)

Accepted Answer

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

Question 5

Decide whether the relation defines a function.
-$y = \frac { 1 } { x - 5 }$

Accepted Answer

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

Question 6

The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport.  
-During which two hour period did the temperature increase the most?

Accepted Answer

A)  10 a.m. to 11 a.m. 
B)  10 a.m. to 12 p.m. 
C)  12 p.m. to 2 p.m. 
D)  9 a.m. to 11 a.m. 
A)  10 a.m. to 11 a.m. 
B)  10 a.m. to 12 p.m. 
C)  12 p.m. to 2 p.m. 
D)  9 a.m. to 11 a.m.

Question 7

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

Accepted Answer

A)  y = 2x + 7 
B)  2x - 4y = 7 
C)  x = 2 
D)  f(x) = -4x + 2 
A)  y = 2x + 7 
B)  2x - 4y = 7 
C)  x = 2 
D)  f(x) = -4x + 2

Question 8

Determine whether (f  g)(x) = x and whether (g  f)(x) = x.
-$$f ( x ) = \sqrt [ 5 ] { x - 14 } , g ( x ) = x ^ { 5 } + 14$$

Accepted Answer

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

Question 9

The graph of y = f(x) is given. Use the graph to find the function value.
-  Find f(-4).

Accepted Answer

A)  None of these 
B)  1 
C)  -4 
D)  1.8 
A)  None of these 
B)  1 
C)  -4 
D)  1.8

Question 10

Find the center and radius of the circle.
-$$x ^ { 2 } + y ^ { 2 } + 10 x + 14 y + 38 = 0$$

Accepted Answer

A)  center: $( - 5 , - 7 )$; radius: 6 
B)  center: $( 5,7 )$; radius: 36 
C)  center: $( 7,5 )$; radius: 36 
D)  center: $( - 7 , - 5 )$; radius: 6 
A)  center: $( - 5 , - 7 )$; radius: 6 
B)  center: $( 5,7 )$; radius: 36 
C)  center: $( 7,5 )$; radius: 36 
D)  center: $( - 7 , - 5 )$; radius: 6

Question 11

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
-midpoint (0, -5), endpoint (2, -4)

Accepted Answer

A)  (6, -2) 
B)  (0, -8) 
C)  (-2, -6) 
D)  (-2, -3) 
A)  (6, -2) 
B)  (0, -8) 
C)  (-2, -6) 
D)  (-2, -3)

Question 12

Provide an appropriate response.
-If a horizontal line is drawn through the point (5, -2), where will it intersect the y-axis?

Accepted Answer

A)  (0, 5) 
B)  (-2, 0) 
C)  (5, 0) 
D)  (0, -2) 
A)  (0, 5) 
B)  (-2, 0) 
C)  (5, 0) 
D)  (0, -2)

Question 13

Choose the value which could represent the slope of the line. Assume that the scale on the x-axis is the same as the scale
on the y-axis.
-

Accepted Answer

A)  -1 
B)  -4 
C)  1 
D)  4 
A)  -1 
B)  -4 
C)  1 
D)  4

Question 14

For the points P and Q, find the distance d(P, Q).
-$$P ( 5,6 ) , Q ( - 1,3 )$$

Accepted Answer

A)  $27 \sqrt { 3 }$ 
B)  27 
C)  $3 \sqrt { 5 }$ 
D)  3 
A)  $27 \sqrt { 3 }$ 
B)  27 
C)  $3 \sqrt { 5 }$ 
D)  3

Question 15

Graph the circle.
-$$( x - 4 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 25$$

Accepted Answer

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

Question 16

The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport.  
-What temperature was recorded at 4 p.m.?

Accepted Answer

A)  74 ° F 
B)  77 ° F 
C)  78 ° F 
D)  76 ° F 
A)  74 ° F 
B)  77 ° F 
C)  78 ° F 
D)  76 ° F

Question 17

Graph the function.
-

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

Match the equation with the correct graph.
-$$4 x - 3 y = 3$$

Accepted Answer

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

Question 20

Rewrite the equation so that one side is 0, then replace 0 with y. The graph of the equation for y is shown.
Use a graphing calculator to solve the linear equation.
-$$3 ( 2 z - 4 ) = 5 ( z + 3 )$$

Accepted Answer

A)  $\{ 27 \}$ 
B)  $\{ 6 \}$ 
C)  $\{ - 3 \}$ 
D)  $\{ 3 \}$ 
A)  $\{ 27 \}$ 
B)  $\{ 6 \}$ 
C)  $\{ - 3 \}$ 
D)  $\{ 3 \}$

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - $x ^ { 2 } + y ^ { 2 } - 6 x + 8 y + 25 = 0$

Give the domain and range of the relation. -

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - $\mathrm { P } ( 11 \sqrt { 5 } , - \sqrt { 10 } ) , \mathrm { Q } ( - \sqrt { 5 } , 0 )$

Determine whether the three points are collinear. -(5, 11), (-3, 6), (10, 19)

Decide whether the relation defines a function. - $y = \frac { 1 } { x - 5 }$

The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport. -During which two hour period did the temperature increase the most?

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

Determine whether (f  g)(x) = x and whether (g  f)(x) = x. - $f ( x ) = \sqrt [ 5 ] { x - 14 } , g ( x ) = x ^ { 5 } + 14$

The graph of y = f(x) is given. Use the graph to find the function value. - Find f(-4).

Find the center and radius of the circle. - $x ^ { 2 } + y ^ { 2 } + 10 x + 14 y + 38 = 0$

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint (0, -5), endpoint (2, -4)

Provide an appropriate response. -If a horizontal line is drawn through the point (5, -2), where will it intersect the y-axis?

Choose the value which could represent the slope of the line. Assume that the scale on the x-axis is the same as the scale on the y-axis. -

For the points P and Q, find the distance d(P, Q). - $P ( 5,6 ) , Q ( - 1,3 )$

Graph the circle. - $( x - 4 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 25$ $Graph the circle. - ( x - 4 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 25$

The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport. -What temperature was recorded at 4 p.m.?

Graph the function. -

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

Match the equation with the correct graph. - $4 x - 3 y = 3$

Rewrite the equation so that one side is 0, then replace 0 with y. The graph of the equation for y is shown. Use a graphing calculator to solve the linear equation. - $3 ( 2 z - 4 ) = 5 ( z + 3 )$

Review of Basic Concepts

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

Filters

Exam 3: Graphs and Functions

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - x2+y2−6x+8y+25=0x ^ { 2 } + y ^ { 2 } - 6 x + 8 y + 25 = 0x2+y2−6x+8y+25=0

Give the domain and range of the relation. -

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - P(115,−10),Q(−5,0)\mathrm { P } ( 11 \sqrt { 5 } , - \sqrt { 10 } ) , \mathrm { Q } ( - \sqrt { 5 } , 0 )P(115​,−10​),Q(−5​,0)

Determine whether the three points are collinear. -(5, 11), (-3, 6), (10, 19)

Decide whether the relation defines a function. - y=1x−5y = \frac { 1 } { x - 5 }y=x−51​

The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport. -During which two hour period did the temperature increase the most?

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

Determine whether (f  g)(x) = x and whether (g  f)(x) = x. - f(x)=x−145,g(x)=x5+14f ( x ) = \sqrt [ 5 ] { x - 14 } , g ( x ) = x ^ { 5 } + 14f(x)=5x−14​,g(x)=x5+14

The graph of y = f(x) is given. Use the graph to find the function value. - Find f(-4).

Find the center and radius of the circle. - x2+y2+10x+14y+38=0x ^ { 2 } + y ^ { 2 } + 10 x + 14 y + 38 = 0x2+y2+10x+14y+38=0

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint (0, -5), endpoint (2, -4)

Provide an appropriate response. -If a horizontal line is drawn through the point (5, -2), where will it intersect the y-axis?

Choose the value which could represent the slope of the line. Assume that the scale on the x-axis is the same as the scale on the y-axis. -

For the points P and Q, find the distance d(P, Q). - P(5,6),Q(−1,3)P ( 5,6 ) , Q ( - 1,3 )P(5,6),Q(−1,3)

Graph the circle. - (x−4)2+(y+1)2=25( x - 4 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 25(x−4)2+(y+1)2=25

The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport. -What temperature was recorded at 4 p.m.?

Graph the function. -

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

Match the equation with the correct graph. - 4x−3y=34 x - 3 y = 34x−3y=3

Rewrite the equation so that one side is 0, then replace 0 with y. The graph of the equation for y is shown. Use a graphing calculator to solve the linear equation. - 3(2z−4)=5(z+3)3 ( 2 z - 4 ) = 5 ( z + 3 )3(2z−4)=5(z+3)

Review of Basic Concepts

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

Filters

Decide whether or not the equation has a circle as its graph. If it does not, describe the graph. - $x ^ { 2 } + y ^ { 2 } - 6 x + 8 y + 25 = 0$

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - $\mathrm { P } ( 11 \sqrt { 5 } , - \sqrt { 10 } ) , \mathrm { Q } ( - \sqrt { 5 } , 0 )$

Decide whether the relation defines a function. - $y = \frac { 1 } { x - 5 }$

Determine whether (f  g)(x) = x and whether (g  f)(x) = x. - $f ( x ) = \sqrt [ 5 ] { x - 14 } , g ( x ) = x ^ { 5 } + 14$

Find the center and radius of the circle. - $x ^ { 2 } + y ^ { 2 } + 10 x + 14 y + 38 = 0$

For the points P and Q, find the distance d(P, Q). - $P ( 5,6 ) , Q ( - 1,3 )$

Graph the circle. - $( x - 4 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 25$ $Graph the circle. - ( x - 4 ) ^ { 2 } + ( y + 1 ) ^ { 2 } = 25$

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

Match the equation with the correct graph. - $4 x - 3 y = 3$

Rewrite the equation so that one side is 0, then replace 0 with y. The graph of the equation for y is shown. Use a graphing calculator to solve the linear equation. - $3 ( 2 z - 4 ) = 5 ( z + 3 )$