Question 1

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)  $- 2$ 
B)  2 
C)  0 
D)  undefined 
A)  $- 2$ 
B)  2 
C)  0 
D)  undefined

Question 2

Graph the line described.
-through $( 0,4 ) ; \mathrm { m } = \frac { 1 } { 3 }$

Accepted Answer

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

Question 3

Use a graphing calculator to solve the linear equation.
-The graph of $y _ { 1 }$ is shown in the standard viewing window. Which is the only choice that could possibly be the solution of the equation $\mathrm { y } _ { 1 } = 0$ ?

$$- 5,5 , \frac { 16 } { 3 } , 15$$

Accepted Answer

A)  $- 5$ 
B)  5 
C)  15 
D)  $\frac { 16 } { 3 }$ 
A)  $- 5$ 
B)  5 
C)  15 
D)  $\frac { 16 } { 3 }$

Question 4

Match the equation with the correct graph.
-$$9 x + 4 y = - 12$$

Accepted Answer

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

Question 5

Match the equation with the correct graph.
-$$\mathrm { y } = - 1$$

Accepted Answer

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

Question 6

Find the specified domain.
-Find the domain of $( f g ) ( x )$ when $f ( x ) = \frac { 2 } { x - 9 }$ and $g ( x ) = - 3 x - 5$

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $( - \infty , 5 ) \cup ( 5 , \infty )$ 
C)  $( - \infty , 9 ) \cup ( 9 , \infty )$ 
D)  $( - \infty , - 9 ) \cup ( - 9 , \infty )$ 
A)  $( - \infty , \infty )$ 
B)  $( - \infty , 5 ) \cup ( 5 , \infty )$ 
C)  $( - \infty , 9 ) \cup ( 9 , \infty )$ 
D)  $( - \infty , - 9 ) \cup ( - 9 , \infty )$

Question 7

Solve the problem. 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.
 
Determine a linear function f defined by f(x) = mx + b that models the data using (1, 1340) and (6, 3045).

Accepted Answer

A)  $f ( x ) = 1340$ 
B)  $f ( x ) = 2781 - 1441 x$ 
C)  $f ( x ) = 999 x + 341$ 
D)  $f ( x ) = 341 x + 999$ 
A)  $f ( x ) = 1340$ 
B)  $f ( x ) = 2781 - 1441 x$ 
C)  $f ( x ) = 999 x + 341$ 
D)  $f ( x ) = 341 x + 999$

Question 8

For the points P and Q, find the distance d(P, Q).
-$\mathrm { P } ( 3 \sqrt { 5 } , - 5 \sqrt { 11 } ) , \mathrm { Q } ( 4 \sqrt { 5 } , 3 \sqrt { 11 } )$

Accepted Answer

A)  709 
B)  $\sqrt { 83 }$ 
C)  83 
D)  $\sqrt { 709 }$ 
A)  709 
B)  $\sqrt { 83 }$ 
C)  83 
D)  $\sqrt { 709 }$

Question 9

Determine whether (f ∘ g)(x) = x and whether (g ∘ f)(x) = x.
-$$f ( x ) = \frac { 1 } { x } , g ( x ) = x$$

Accepted Answer

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

Question 10

Find the specified domain.
-Find the domain of $( f - g ) ( x )$ when $f ( x ) = 2 x - 5$ and $g ( x ) = 6 x - 3$.

Accepted Answer

A)  $( - 5,2 )$ 
B)  $( - 2 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $( - 2,5 )$ 
A)  $( - 5,2 )$ 
B)  $( - 2 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $( - 2,5 )$

Question 11

Decide whether the relation defines a function.
-

Accepted Answer

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

Question 12

Graph the line described.
-$\text { through }(-5,7) ; m=0$

Accepted Answer

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

Question 13

Provide an appropriate response.
-What is the distance from the point $( c , z )$ to the point $( m , q ) ?$

Accepted Answer

A)  $\sqrt { ( m - c ) ^ { 2 } - ( q - z ) ^ { 2 } }$ 
B)  $[ \sqrt { m - c } + \sqrt { q - z } ] ^ { 2 }$ 
C)  $\sqrt { ( m - c ) ^ { 2 } + ( q - z ) ^ { 2 } }$ 
D)  $\sqrt { ( c - z ) ^ { 2 } + ( m - q ) ^ { 2 } }$ 
A)  $\sqrt { ( m - c ) ^ { 2 } - ( q - z ) ^ { 2 } }$ 
B)  $[ \sqrt { m - c } + \sqrt { q - z } ] ^ { 2 }$ 
C)  $\sqrt { ( m - c ) ^ { 2 } + ( q - z ) ^ { 2 } }$ 
D)  $\sqrt { ( c - z ) ^ { 2 } + ( m - q ) ^ { 2 } }$

Question 14

Graph the function.
-$y=(x+7)^{2}-5$

Accepted Answer

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

Question 15

Give the domain and range of the relation.
-$$y = 4 x ^ { 6 }$$

Accepted Answer

A)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
B)  domain: $[ 0 , \infty )$; range: $[ - 4 , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $[ 4 , \infty )$ 
D)  domain: $( - \infty , \infty )$; range: $[ 0 , \infty )$ 
A)  domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$ 
B)  domain: $[ 0 , \infty )$; range: $[ - 4 , \infty )$ 
C)  domain: $( - \infty , \infty )$; range: $[ 4 , \infty )$ 
D)  domain: $( - \infty , \infty )$; range: $[ 0 , \infty )$

Question 16

Solve the problem. Write all linear equations in slope-intercept form.
-By reading a graph on defense spending in the country of Warpeas, you discover that in year 0 the country spent $144 million on defense and in year 8 spent $528 million. Write a linear function that
Relates y (in millions of dollars) to x.

Accepted Answer

A)  $y = - 48 x - 144$ 
B)  $y = 84 x + 144$ 
C)  $y = 48 x + 144$ 
D)  $y = \frac { 1 } { 3 } x + 144$ 
A)  $y = - 48 x - 144$ 
B)  $y = 84 x + 144$ 
C)  $y = 48 x + 144$ 
D)  $y = \frac { 1 } { 3 } x + 144$

Question 17

For the points P and Q, find the coordinates of the midpoint of the segment PQ.
-$$\mathrm { P } ( - 2 , - 8 ) , \mathrm { Q } ( 5,5 )$$

Accepted Answer

A)  $( 3 , - 3 )$ 
B)  $\left( \frac { 3 } { 2 } , - \frac { 3 } { 2 } \right)$ 
C)  $( - 7 , - 13 )$ 
D)  $\left( - \frac { 7 } { 2 } , - \frac { 13 } { 2 } \right)$ 
A)  $( 3 , - 3 )$ 
B)  $\left( \frac { 3 } { 2 } , - \frac { 3 } { 2 } \right)$ 
C)  $( - 7 , - 13 )$ 
D)  $\left( - \frac { 7 } { 2 } , - \frac { 13 } { 2 } \right)$

Question 18

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such.
-$g(x)=x-4$

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 19

Solve the problem.
-A faucet is used to add water to a large bottle that already contained some water. After it has been filling for 5 seconds, the gauge on the bottle indicates that it contains 14 ounces of water. After it has been filling for 11 seconds, the gauge indicates the bottle contains 26 ounces of water. Find and interpret the average rate of change in the volume of water per second.

Accepted Answer

A)  4 ounces per second; the average rate of change in the volume of water is 4 ounces per second. 
B)  15 ounces per second; the average rate of change in the volume of water is 15 ounces per second. 
C)  $\frac { 1 } { 2 }$ ounce per second; the average rate of change in the volume of water is $\frac { 1 } { 2 }$ ounce per second. 
D)  2 ounces per second; the average rate of change in the volume of water is 2 ounces per second. 
A)  4 ounces per second; the average rate of change in the volume of water is 4 ounces per second. 
B)  15 ounces per second; the average rate of change in the volume of water is 15 ounces per second. 
C)  $\frac { 1 } { 2 }$ ounce per second; the average rate of change in the volume of water is $\frac { 1 } { 2 }$ ounce per second. 
D)  2 ounces per second; the average rate of change in the volume of water is 2 ounces per second.

Question 20

Decide whether the relation defines a function.
-$$\{ ( - 8,1 ) , ( - 3 , - 6 ) , ( 3 , - 4 ) , ( 3,3 ) \}$$

Accepted Answer

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

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. -

Graph the line described. -through $( 0,4 ) ; \mathrm { m } = \frac { 1 } { 3 }$ $Graph the line described. -through ( 0,4 ) ; \mathrm { m } = \frac { 1 } { 3 }$

Match the equation with the correct graph. - $9 x + 4 y = - 12$

Match the equation with the correct graph. - $\mathrm { y } = - 1$

Find the specified domain. -Find the domain of $( f g ) ( x )$ when $f ( x ) = \frac { 2 } { x - 9 }$ and $g ( x ) = - 3 x - 5$

For the points P and Q, find the distance d(P, Q). - $\mathrm { P } ( 3 \sqrt { 5 } , - 5 \sqrt { 11 } ) , \mathrm { Q } ( 4 \sqrt { 5 } , 3 \sqrt { 11 } )$

Determine whether (f ∘ g)(x) = x and whether (g ∘ f)(x) = x. - $f ( x ) = \frac { 1 } { x } , g ( x ) = x$

Find the specified domain. -Find the domain of $( f - g ) ( x )$ when $f ( x ) = 2 x - 5$ and $g ( x ) = 6 x - 3$ .

Decide whether the relation defines a function. -

Graph the line described. - $\text { through }(-5,7) ; m=0$ $Graph the line described. - \text { through }(-5,7) ; m=0$

Provide an appropriate response. -What is the distance from the point $( c , z )$ to the point $( m , q ) ?$

Graph the function. - $y=(x+7)^{2}-5$ $Graph the function. - y=(x+7)^{2}-5$

Give the domain and range of the relation. - $y = 4 x ^ { 6 }$

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - $\mathrm { P } ( - 2 , - 8 ) , \mathrm { Q } ( 5,5 )$

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. - $g(x)=x-4$

Decide whether the relation defines a function. - $\{ ( - 8,1 ) , ( - 3 , - 6 ) , ( 3 , - 4 ) , ( 3,3 ) \}$

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

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. -

Graph the line described. -through (0,4);m=13( 0,4 ) ; \mathrm { m } = \frac { 1 } { 3 }(0,4);m=31​

Match the equation with the correct graph. - 9x+4y=−129 x + 4 y = - 129x+4y=−12

Match the equation with the correct graph. - y=−1\mathrm { y } = - 1y=−1

Find the specified domain. -Find the domain of (fg)(x)( f g ) ( x )(fg)(x) when f(x)=2x−9f ( x ) = \frac { 2 } { x - 9 }f(x)=x−92​ and g(x)=−3x−5g ( x ) = - 3 x - 5g(x)=−3x−5

For the points P and Q, find the distance d(P, Q). - P(35,−511),Q(45,311)\mathrm { P } ( 3 \sqrt { 5 } , - 5 \sqrt { 11 } ) , \mathrm { Q } ( 4 \sqrt { 5 } , 3 \sqrt { 11 } )P(35​,−511​),Q(45​,311​)

Determine whether (f ∘ g)(x) = x and whether (g ∘ f)(x) = x. - f(x)=1x,g(x)=xf ( x ) = \frac { 1 } { x } , g ( x ) = xf(x)=x1​,g(x)=x

Find the specified domain. -Find the domain of (f−g)(x)( f - g ) ( x )(f−g)(x) when f(x)=2x−5f ( x ) = 2 x - 5f(x)=2x−5 and g(x)=6x−3g ( x ) = 6 x - 3g(x)=6x−3 .

Decide whether the relation defines a function. -

Graph the line described. - through (−5,7);m=0\text { through }(-5,7) ; m=0 through (−5,7);m=0

Provide an appropriate response. -What is the distance from the point (c,z)( c , z )(c,z) to the point (m,q)?( m , q ) ?(m,q)?

Graph the function. - y=(x+7)2−5y=(x+7)^{2}-5y=(x+7)2−5

Give the domain and range of the relation. - y=4x6y = 4 x ^ { 6 }y=4x6

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - P(−2,−8),Q(5,5)\mathrm { P } ( - 2 , - 8 ) , \mathrm { Q } ( 5,5 )P(−2,−8),Q(5,5)

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. - g(x)=x−4g(x)=x-4g(x)=x−4

Decide whether the relation defines a function. - {(−8,1),(−3,−6),(3,−4),(3,3)}\{ ( - 8,1 ) , ( - 3 , - 6 ) , ( 3 , - 4 ) , ( 3,3 ) \}{(−8,1),(−3,−6),(3,−4),(3,3)}

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

Graph the line described. -through $( 0,4 ) ; \mathrm { m } = \frac { 1 } { 3 }$ $Graph the line described. -through ( 0,4 ) ; \mathrm { m } = \frac { 1 } { 3 }$

Match the equation with the correct graph. - $9 x + 4 y = - 12$

Match the equation with the correct graph. - $\mathrm { y } = - 1$

Find the specified domain. -Find the domain of $( f g ) ( x )$ when $f ( x ) = \frac { 2 } { x - 9 }$ and $g ( x ) = - 3 x - 5$

For the points P and Q, find the distance d(P, Q). - $\mathrm { P } ( 3 \sqrt { 5 } , - 5 \sqrt { 11 } ) , \mathrm { Q } ( 4 \sqrt { 5 } , 3 \sqrt { 11 } )$

Determine whether (f ∘ g)(x) = x and whether (g ∘ f)(x) = x. - $f ( x ) = \frac { 1 } { x } , g ( x ) = x$

Find the specified domain. -Find the domain of $( f - g ) ( x )$ when $f ( x ) = 2 x - 5$ and $g ( x ) = 6 x - 3$ .

Graph the line described. - $\text { through }(-5,7) ; m=0$ $Graph the line described. - \text { through }(-5,7) ; m=0$

Provide an appropriate response. -What is the distance from the point $( c , z )$ to the point $( m , q ) ?$

Graph the function. - $y=(x+7)^{2}-5$ $Graph the function. - y=(x+7)^{2}-5$

Give the domain and range of the relation. - $y = 4 x ^ { 6 }$

For the points P and Q, find the coordinates of the midpoint of the segment PQ. - $\mathrm { P } ( - 2 , - 8 ) , \mathrm { Q } ( 5,5 )$

Graph the linear function and give the domain and the range. If the function is a constant function, identify it as such. - $g(x)=x-4$

Decide whether the relation defines a function. - $\{ ( - 8,1 ) , ( - 3 , - 6 ) , ( 3 , - 4 ) , ( 3,3 ) \}$