Question 1

An equation that defines y as a function of x is given. Solve for y in terms of x, and replace y with the function notation
f(x).
-$$x - 5 y = 35$$

Accepted Answer

A)  $f ( x ) = \frac { 1 } { 5 } x - 35$ 
B)  $f ( x ) = - x + 7$ 
C)  $f ( x ) = - \frac { 1 } { 5 } x + 7$ 
D)  $f ( x ) = \frac { 1 } { 5 } x - 7$ 
A)  $f ( x ) = \frac { 1 } { 5 } x - 35$ 
B)  $f ( x ) = - x + 7$ 
C)  $f ( x ) = - \frac { 1 } { 5 } x + 7$ 
D)  $f ( x ) = \frac { 1 } { 5 } x - 7$

Question 2

Write an equation for the line described. Give your answer in slope-intercept form.
-through (-4, 5), m = 0

Accepted Answer

A)  x = -4 
B) x = 5 
C) y = 5 
D) y = -4 
A)  x = -4 
B) x = 5 
C) y = 5 
D) y = -4

Question 3

Graph the circle.
-$$x ^ { 2 } + y ^ { 2 } = 81$$

Accepted Answer

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

Question 4

Solve the problem.
-An investment is worth $\$ 2857$ in year 0, the initial investment year. By year 4 its value has increased to $\$ 3373$. Let $y$ be the value of the investment in the year $x$. Find and interpret the average rate of change in value per year.

Accepted Answer

A)  - $\$ 129$ per year; the value of the investment decreases by $\$ 129$ per year during these years. 
B)  $\$ 2857$ per year; the value of the investment increases by $\$ 2857$ per year during these years. 
C)  $\$ 129$ per year; the value of the investment increases by $\$ 129$ per year during these years. 
D)  $\$ 3889$ per year; the value of the investment increases by $\$ 3889$ per year during these years. 
A)  - $\$ 129$ per year; the value of the investment decreases by $\$ 129$ per year during these years. 
B)  $\$ 2857$ per year; the value of the investment increases by $\$ 2857$ per year during these years. 
C)  $\$ 129$ per year; the value of the investment increases by $\$ 129$ per year during these years. 
D)  $\$ 3889$ per year; the value of the investment increases by $\$ 3889$ per year during these years.

Question 5

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)  $y = - \frac { 1 } { 5 } x$ 
B)  $y = - 5 x$ 
C)  $y = \frac { 1 } { 5 } x$ 
D)  $y = 5 x$ 
A)  $y = - \frac { 1 } { 5 } x$ 
B)  $y = - 5 x$ 
C)  $y = \frac { 1 } { 5 } x$ 
D)  $y = 5 x$

Question 6

For the pair of functions, find the indicated sum, difference, product, or quotient.
-$$f ( x ) = x ^ { 2 } + 1 , g ( x ) = 2 x + 5$$
Find $( f g ) ( x )$.

Accepted Answer

A)  $2 x ^ { 2 } + 2 x + 5$ 
B)  $2 x ^ { 3 } + 5 x ^ { 2 } + 2 x + 5$ 
C)  $2 x ^ { 3 } + 2 x ^ { 2 } + 5 x + 5$ 
D)  $2 x ^ { 3 } + 5$ 
A)  $2 x ^ { 2 } + 2 x + 5$ 
B)  $2 x ^ { 3 } + 5 x ^ { 2 } + 2 x + 5$ 
C)  $2 x ^ { 3 } + 2 x ^ { 2 } + 5 x + 5$ 
D)  $2 x ^ { 3 } + 5$

Question 7

Graph the point symmetric to the given point.
-Plot the point (3, 0), then plot the point that is symmetric to (3, 0) with respect to the origin.

Accepted Answer

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

Question 8

Graph the function.
-

Accepted Answer

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

Question 9

Use the graph to solve the problem.
-During which two hour period did the temperature increase the most?

Accepted Answer

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

Question 10

Evaluate the function.
-Find $f ( k - 1 )$ when $f ( x ) = 4 x ^ { 2 } - 2 x - 1$

Accepted Answer

A)  $4 k ^ { 2 } - 6 k + 1$ 
B)  $4 \mathrm { k } ^ { 2 } - 10 \mathrm { k } + 1$ 
C)  $4 k ^ { 2 } - 10 k + 5$ 
D)  $- 10 \mathrm { k } ^ { 2 } + 4 \mathrm { k } + 5$ 
A)  $4 k ^ { 2 } - 6 k + 1$ 
B)  $4 \mathrm { k } ^ { 2 } - 10 \mathrm { k } + 1$ 
C)  $4 k ^ { 2 } - 10 k + 5$ 
D)  $- 10 \mathrm { k } ^ { 2 } + 4 \mathrm { k } + 5$

Question 11

Determine whether the three points are collinear.
-(-5, -11), (4, 7), (5, 9)

Accepted Answer

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

Question 12

Find the center and radius of the circle.
-$$x ^ { 2 } + y ^ { 2 } - 16 x + 8 y + 55 = 0$$

Accepted Answer

A)  center: (4, -8); radius: 25 
B)  center: (-4, 8); radius: 5 
C)  center: (-8, 4); radius: 25 
D)  center: (8, -4); radius: 5 
A)  center: (4, -8); radius: 25 
B)  center: (-4, 8); radius: 5 
C)  center: (-8, 4); radius: 25 
D)  center: (8, -4); radius: 5

Question 13

Find the center and radius of the circle.
-$$x ^ { 2 } + y ^ { 2 } - 2 x + 6 y - 6 = 0$$

Accepted Answer

A)  center: (-3, 1); radius: 4 
B)  center: (3, -1); radius: 16 
C)  center: (-1, 3); radius: 16 
D)  center: (1, -3); radius: 4 
A)  center: (-3, 1); radius: 4 
B)  center: (3, -1); radius: 16 
C)  center: (-1, 3); radius: 16 
D)  center: (1, -3); radius: 4

Question 14

Provide an appropriate response.
-What is the distance from the origin to the point $( m , - n )$ ?

Accepted Answer

A)  $\sqrt { m - n }$ 
B)  $\sqrt { m ^ { 2 } - n ^ { 2 } }$ 
C)  $m ^ { 2 } + n ^ { 2 }$ 
D)  $\sqrt { m ^ { 2 } + n ^ { 2 } }$ 
A)  $\sqrt { m - n }$ 
B)  $\sqrt { m ^ { 2 } - n ^ { 2 } }$ 
C)  $m ^ { 2 } + n ^ { 2 }$ 
D)  $\sqrt { m ^ { 2 } + n ^ { 2 } }$

Question 15

An equation that defines y as a function of x is given. Solve for y in terms of x, and replace y with the function notation
f(x).
-$$x + 6 y = 8$$

Accepted Answer

A)  $f ( x ) = \frac { 1 } { 6 } x + \frac { 4 } { 3 }$ 
B)  $f ( x ) = - x + \frac { 4 } { 3 }$ 
C)  $f ( x ) = - \frac { 1 } { 6 } x + \frac { 4 } { 3 }$ 
D)  $f ( x ) = 6 x - 8$ 
A)  $f ( x ) = \frac { 1 } { 6 } x + \frac { 4 } { 3 }$ 
B)  $f ( x ) = - x + \frac { 4 } { 3 }$ 
C)  $f ( x ) = - \frac { 1 } { 6 } x + \frac { 4 } { 3 }$ 
D)  $f ( x ) = 6 x - 8$

Question 16

Find the slope and the y-intercept of the line.
-$$x + 3 y = - 5$$

Accepted Answer

A)  slope: $- \frac { 1 } { 3 } ; \mathrm { y }$-intercept: $- \frac { 5 } { 3 }$ 
B)  slope: $\frac { 1 } { 3 } ; y - i n t e r c e p t : - \frac { 5 } { 3 }$ 
C)  slope: $- \frac { 5 } { 3 } ; y$-intercept: $- \frac { 1 } { 3 }$ 
D)  slope: $- 3 ; y$-intercept: $- 5$ 
A)  slope: $- \frac { 1 } { 3 } ; \mathrm { y }$-intercept: $- \frac { 5 } { 3 }$ 
B)  slope: $\frac { 1 } { 3 } ; y - i n t e r c e p t : - \frac { 5 } { 3 }$ 
C)  slope: $- \frac { 5 } { 3 } ; y$-intercept: $- \frac { 1 } { 3 }$ 
D)  slope: $- 3 ; y$-intercept: $- 5$

Question 17

Decide whether the relation defines a function.
-

Accepted Answer

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

Question 18

For the points P and Q, find the distance d(P, Q).
-$$\mathrm { P } ( 7 , - 1 ) , \mathrm { Q } ( - 5 , - 7 )$$

Accepted Answer

A)  108 
B)  $108 \sqrt { 3 }$ 
C)  6 
D)  $6 \sqrt { 5 }$ 
A)  108 
B)  $108 \sqrt { 3 }$ 
C)  6 
D)  $6 \sqrt { 5 }$

Question 19

Graph the line and give the domain and the range.
-$y=3$

Accepted Answer

A)  $D = \{ 3 \} , \quad R = ( - \infty , \infty )$
  
B)  $\mathrm { D } = \{ 3 \} , \quad \mathrm { R } = ( - \infty , \infty )$
  
C)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = \{ 3 \}$
  
D)  $\mathrm { D } = ( - \infty , \infty ) , \quad \mathrm { R } = \{ 3 \}$
  
A)  $D = \{ 3 \} , \quad R = ( - \infty , \infty )$
  
B)  $\mathrm { D } = \{ 3 \} , \quad \mathrm { R } = ( - \infty , \infty )$
  
C)  $\mathrm { D } = ( - \infty , \infty ) , \mathrm { R } = \{ 3 \}$
  
D)  $\mathrm { D } = ( - \infty , \infty ) , \quad \mathrm { R } = \{ 3 \}$

Question 20

The graph of a linear function f is shown. Identify the slope, y-intercept, and x-intercept.
-

Accepted Answer

A)  $- \frac { 1 } { 3 } ; 3,9$ 
B)  $- 3 ; 3,9$ 
C)  $\frac { 1 } { 3 } ; 3,9$ 
D)  $- \frac { 1 } { 3 } ; 9,3$ 
A)  $- \frac { 1 } { 3 } ; 3,9$ 
B)  $- 3 ; 3,9$ 
C)  $\frac { 1 } { 3 } ; 3,9$ 
D)  $- \frac { 1 } { 3 } ; 9,3$

An equation that defines y as a function of x is given. Solve for y in terms of x, and replace y with the function notation f(x). - $x - 5 y = 35$

Write an equation for the line described. Give your answer in slope-intercept form. -through (-4, 5), m = 0

Graph the circle. - $x ^ { 2 } + y ^ { 2 } = 81$ $Graph the circle. - x ^ { 2 } + y ^ { 2 } = 81$

Solve the problem. -An investment is worth $\$ 2857$ in year 0, the initial investment year. By year 4 its value has increased to $\$ 3373$ . Let $y$ be the value of the investment in the year $x$ . Find and interpret the average rate of change in value per year.

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

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = x ^ { 2 } + 1 , g ( x ) = 2 x + 5$ Find $( f g ) ( x )$ .

Graph the point symmetric to the given point. -Plot the point (3, 0), then plot the point that is symmetric to (3, 0) with respect to the origin.

Graph the function. -

Use the graph to solve the problem. -During which two hour period did the temperature increase the most?

Evaluate the function. -Find $f ( k - 1 )$ when $f ( x ) = 4 x ^ { 2 } - 2 x - 1$

Determine whether the three points are collinear. -(-5, -11), (4, 7), (5, 9)

Find the center and radius of the circle. - $x ^ { 2 } + y ^ { 2 } - 16 x + 8 y + 55 = 0$

Find the center and radius of the circle. - $x ^ { 2 } + y ^ { 2 } - 2 x + 6 y - 6 = 0$

Provide an appropriate response. -What is the distance from the origin to the point $( m , - n )$ ?

An equation that defines y as a function of x is given. Solve for y in terms of x, and replace y with the function notation f(x). - $x + 6 y = 8$

Find the slope and the y-intercept of the line. - $x + 3 y = - 5$

Decide whether the relation defines a function. -

For the points P and Q, find the distance d(P, Q). - $\mathrm { P } ( 7 , - 1 ) , \mathrm { Q } ( - 5 , - 7 )$

Graph the line and give the domain and the range. - $y=3$

The graph of a linear function f is shown. Identify the slope, y-intercept, and x-intercept. -

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

An equation that defines y as a function of x is given. Solve for y in terms of x, and replace y with the function notation f(x). - x−5y=35x - 5 y = 35x−5y=35

Write an equation for the line described. Give your answer in slope-intercept form. -through (-4, 5), m = 0

Graph the circle. - x2+y2=81x ^ { 2 } + y ^ { 2 } = 81x2+y2=81

Solve the problem. -An investment is worth $2857\$ 2857$2857 in year 0, the initial investment year. By year 4 its value has increased to $3373\$ 3373$3373 . Let yyy be the value of the investment in the year xxx . Find and interpret the average rate of change in value per year.

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

For the pair of functions, find the indicated sum, difference, product, or quotient. - f(x)=x2+1,g(x)=2x+5f ( x ) = x ^ { 2 } + 1 , g ( x ) = 2 x + 5f(x)=x2+1,g(x)=2x+5 Find (fg)(x)( f g ) ( x )(fg)(x) .

Graph the point symmetric to the given point. -Plot the point (3, 0), then plot the point that is symmetric to (3, 0) with respect to the origin.

Graph the function. -

Use the graph to solve the problem. -During which two hour period did the temperature increase the most?

Evaluate the function. -Find f(k−1)f ( k - 1 )f(k−1) when f(x)=4x2−2x−1f ( x ) = 4 x ^ { 2 } - 2 x - 1f(x)=4x2−2x−1

Determine whether the three points are collinear. -(-5, -11), (4, 7), (5, 9)

Find the center and radius of the circle. - x2+y2−16x+8y+55=0x ^ { 2 } + y ^ { 2 } - 16 x + 8 y + 55 = 0x2+y2−16x+8y+55=0

Find the center and radius of the circle. - x2+y2−2x+6y−6=0x ^ { 2 } + y ^ { 2 } - 2 x + 6 y - 6 = 0x2+y2−2x+6y−6=0

Provide an appropriate response. -What is the distance from the origin to the point (m,−n)( m , - n )(m,−n) ?

An equation that defines y as a function of x is given. Solve for y in terms of x, and replace y with the function notation f(x). - x+6y=8x + 6 y = 8x+6y=8

Find the slope and the y-intercept of the line. - x+3y=−5x + 3 y = - 5x+3y=−5

Decide whether the relation defines a function. -

For the points P and Q, find the distance d(P, Q). - P(7,−1),Q(−5,−7)\mathrm { P } ( 7 , - 1 ) , \mathrm { Q } ( - 5 , - 7 )P(7,−1),Q(−5,−7)

Graph the line and give the domain and the range. - y=3y=3y=3

The graph of a linear function f is shown. Identify the slope, y-intercept, and x-intercept. -

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

An equation that defines y as a function of x is given. Solve for y in terms of x, and replace y with the function notation f(x). - $x - 5 y = 35$

Graph the circle. - $x ^ { 2 } + y ^ { 2 } = 81$ $Graph the circle. - x ^ { 2 } + y ^ { 2 } = 81$

Solve the problem. -An investment is worth $\$ 2857$ in year 0, the initial investment year. By year 4 its value has increased to $\$ 3373$ . Let $y$ be the value of the investment in the year $x$ . Find and interpret the average rate of change in value per year.

For the pair of functions, find the indicated sum, difference, product, or quotient. - $f ( x ) = x ^ { 2 } + 1 , g ( x ) = 2 x + 5$ Find $( f g ) ( x )$ .

Evaluate the function. -Find $f ( k - 1 )$ when $f ( x ) = 4 x ^ { 2 } - 2 x - 1$

Find the center and radius of the circle. - $x ^ { 2 } + y ^ { 2 } - 16 x + 8 y + 55 = 0$

Find the center and radius of the circle. - $x ^ { 2 } + y ^ { 2 } - 2 x + 6 y - 6 = 0$

Provide an appropriate response. -What is the distance from the origin to the point $( m , - n )$ ?

An equation that defines y as a function of x is given. Solve for y in terms of x, and replace y with the function notation f(x). - $x + 6 y = 8$

Find the slope and the y-intercept of the line. - $x + 3 y = - 5$

For the points P and Q, find the distance d(P, Q). - $\mathrm { P } ( 7 , - 1 ) , \mathrm { Q } ( - 5 , - 7 )$

Graph the line and give the domain and the range. - $y=3$