Question 1

Determine the x- and y-intercepts for the given function.
-$$g ( x ) = - 7 x - 15$$

Accepted Answer

A)  $x$-intercept: $( 0 , - 15 ) ; y$-intercept: $( 22,0 )$ 
B)  $x$-intercept: $\left( - \frac { 15 } { 7 } , 0 \right) ; y$-intercept: $( 0 , - 15 )$ 
C)  $x$-intercept: $\left( 0 , - \frac { 15 } { 7 } \right) ; y$-intercept: $( - 15,0 )$ 
D)  $x$ - and $y$-intercept: $( 0,0 )$ 
A)  $x$-intercept: $( 0 , - 15 ) ; y$-intercept: $( 22,0 )$ 
B)  $x$-intercept: $\left( - \frac { 15 } { 7 } , 0 \right) ; y$-intercept: $( 0 , - 15 )$ 
C)  $x$-intercept: $\left( 0 , - \frac { 15 } { 7 } \right) ; y$-intercept: $( - 15,0 )$ 
D)  $x$ - and $y$-intercept: $( 0,0 )$

Question 2

Solve the problem.
-The fixed and variable costs to produce an item are given along with the price at which an item is sold. Determine the break-even point. Fixed cost: $\$ 2,093$
Variable cost per items: $\$ 34.50$ Price at which the item is sold: $\$ 80.00$

Accepted Answer

A)  18 items 
B)  61 items 
C)  46 items 
D)  26 items 
A)  18 items 
B)  61 items 
C)  46 items 
D)  26 items

Question 3

Write an equation of the line satisfying the given conditions.
-Passes through (1, 4) and is parallel to the y-axis.

Accepted Answer

A)  y = 1 
B)  y = 4 
C)  x = 4 
D)  x = 1 
A)  y = 1 
B)  y = 4 
C)  x = 4 
D)  x = 1

Question 4

Find the indicated function and write its domain in interval notation.
-$$s ( x ) = \frac { x - 2 } { x ^ { 2 } - 64 } , t ( x ) = \sqrt { x + 8 } , ( s \cdot t ) ( x ) = ?$$

Accepted Answer

A)  $\frac { ( x - 2 ) } { ( x + 8 ) ( x - 8 ) \sqrt { x + 8 } } ; ( - 8,2 ) \cup ( 2,8 ) \cup ( 8 , \infty )$ 
B)  $\frac { ( x - 2 ) \sqrt { x + 8 } } { ( x + 8 ) ( x - 8 ) } ; ( - 8,8 ) \cup ( 8 , \infty )$ 
C)  $\frac { ( x - 2 ) \sqrt { x + 8 } } { ( x + 8 ) ( x - 8 ) } ; ( - 8,2 ) \cup ( 2,8 ) \cup ( 8 , \infty )$ 
D)  $\frac { ( x - 2 ) } { ( x + 8 ) ( x - 8 ) \sqrt { x + 8 } } ; ( - 8,8 ) \cup ( 8 , \infty )$ 
A)  $\frac { ( x - 2 ) } { ( x + 8 ) ( x - 8 ) \sqrt { x + 8 } } ; ( - 8,2 ) \cup ( 2,8 ) \cup ( 8 , \infty )$ 
B)  $\frac { ( x - 2 ) \sqrt { x + 8 } } { ( x + 8 ) ( x - 8 ) } ; ( - 8,8 ) \cup ( 8 , \infty )$ 
C)  $\frac { ( x - 2 ) \sqrt { x + 8 } } { ( x + 8 ) ( x - 8 ) } ; ( - 8,2 ) \cup ( 2,8 ) \cup ( 8 , \infty )$ 
D)  $\frac { ( x - 2 ) } { ( x + 8 ) ( x - 8 ) \sqrt { x + 8 } } ; ( - 8,8 ) \cup ( 8 , \infty )$

Question 5

Evaluate the function for the given value of x.
-$$p ( x ) = x ^ { 2 } + 7 x , q ( x ) = \sqrt { x + 3 } , ( p \cdot q ) ( x ) = ?$$

Accepted Answer

A)  $x + 3 + 7 \sqrt { x + 3 }$ 
B)  $( p \cdot q ) ( x ) = \sqrt { \left( x ^ { 2 } + 7 x \right) ( x + 3 ) }$ 
C)  $( p \cdot q ) ( x ) = \left( x ^ { 2 } + 7 x \right) \sqrt { x + 3 }$ 
D)  $( p \cdot q ) ( x ) = x ^ { 2 } + 7 x \cdot \sqrt { x + 3 }$ 
A)  $x + 3 + 7 \sqrt { x + 3 }$ 
B)  $( p \cdot q ) ( x ) = \sqrt { \left( x ^ { 2 } + 7 x \right) ( x + 3 ) }$ 
C)  $( p \cdot q ) ( x ) = \left( x ^ { 2 } + 7 x \right) \sqrt { x + 3 }$ 
D)  $( p \cdot q ) ( x ) = x ^ { 2 } + 7 x \cdot \sqrt { x + 3 }$

Question 6

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-Suppose that $y = C ( x )$ represents the cost to produce $x$ items, and that $y = R ( x )$ represents the revenue for selling $x$ items. The profit $P ( x )$ of producing and selling $x$ items is defined by $P ( x ) =$ .

Accepted Answer

The answer of Write the word or phrase that best...

Question 7

Write the word or phrase that best completes each statement or answers the question. Provide the missing information.
-Explain what it means for a relation to define y as a function of x.

Accepted Answer

A relation defines y as a func

Question 8

Use transformations to graph the given function.
-$$q ( x ) = \sqrt { 5 x }$$

Accepted Answer

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

Question 9

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-If two nonvertical lines have the same slope but different y-intercepts, then the lines are
(parallel/perpendicular).

Accepted Answer

The answer of Write the word or phrase that best...

Question 10

Write the equation in slope-intercept form. Then, graph the line using the slope and y-intercept.
-$-5 x-2 y=0$

Accepted Answer

A)  $y = - \frac { 5 } { 2 } x$
  
B)  $y = \frac { 2 } { 5 } x$
  
C)  $y = - \frac { 2 } { 5 } x$
  
D)  $y = \frac { 5 } { 2 } x$
  
A)  $y = - \frac { 5 } { 2 } x$
  
B)  $y = \frac { 2 } { 5 } x$
  
C)  $y = - \frac { 2 } { 5 } x$
  
D)  $y = \frac { 5 } { 2 } x$

Question 11

Determine the domain and range of the function.
-

Accepted Answer

A)  Domain: $[ 2 , \infty )$; Range: $( - \infty , \infty )$ 
B)  Domain: $( - \infty , \infty )$; Range: $( - \infty , 2 ]$ 
C)  Domain: $( - \infty , \infty )$; Range: $[ 2 , \infty )$ 
D)  Domain: $( - \infty , 2 ]$; Range: $( - \infty , \infty )$ 
A)  Domain: $[ 2 , \infty )$; Range: $( - \infty , \infty )$ 
B)  Domain: $( - \infty , \infty )$; Range: $( - \infty , 2 ]$ 
C)  Domain: $( - \infty , \infty )$; Range: $[ 2 , \infty )$ 
D)  Domain: $( - \infty , 2 ]$; Range: $( - \infty , \infty )$

Question 12

The slope of a line is given. Find the slope of a line parallel to the given line.
-$$m = \frac { 11 } { 10 }$$

Accepted Answer

A)  $\frac { 10 } { 11 }$ 
B)  $- \frac { 11 } { 10 }$ 
C)  $\frac { 11 } { 10 }$ 
D)  $- \frac { 10 } { 11 }$ 
A)  $\frac { 10 } { 11 }$ 
B)  $- \frac { 11 } { 10 }$ 
C)  $\frac { 11 } { 10 }$ 
D)  $- \frac { 10 } { 11 }$

Question 13

Find the midpoint of the line segment whose endpoints are the given points.
-$( 3,1 )$ and $( 9,4 )$

Accepted Answer

A)  $( - 6,3 )$ 
B)  $\left( 6 , \frac { 5 } { 2 } \right)$ 
C)  $( 12,5 )$ 
D)  $\left( - 3 , \frac { 3 } { 2 } \right)$ 
A)  $( - 6,3 )$ 
B)  $\left( 6 , \frac { 5 } { 2 } \right)$ 
C)  $( 12,5 )$ 
D)  $\left( - 3 , \frac { 3 } { 2 } \right)$

Question 14

Use transformations on the basic functions to write a rule y = f (x) that would produce the given graph.
-

Accepted Answer

A)  $y=|x+1|-2$ 
B)  $y = | x - 2 | + 1$ 
C)  $y = | x + 2 | - 1$ 
D)  $y = | x - 1 | + 2$ 
A)  $y=|x+1|-2$ 
B)  $y = | x - 2 | + 1$ 
C)  $y = | x + 2 | - 1$ 
D)  $y = | x - 1 | + 2$

Question 15

The distance between two distinct points ( $\left( x _ { 1 } , y _ { 1 } \right) \text { and } \left( x _ { 2 } , y _ { 2 } \right)$ ) is given by the formula
.

Accepted Answer

The answer of The distance between two distinct points (...

Question 16

Find the exact distance between the points.
-(-9, 4) and (-5, -6)

Accepted Answer

A)  116 
B)  200 
C)  $10 \sqrt { 2 }$ 
D)  $2 \sqrt { 29 }$ 
A)  116 
B)  200 
C)  $10 \sqrt { 2 }$ 
D)  $2 \sqrt { 29 }$

Question 17

Determine the center and radius of the circle.
-$$( x + 2 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 45$$

Accepted Answer

A)  Center: $( - 2,3 )$; Radius: $3 \sqrt { 5 }$ 
B)  Center: $( - 2,3 )$; Radius: 45 
C)  Center: $( 2 , - 3 )$; Radius: $3 \sqrt { 5 }$ 
D)  Center: $( 2 , - 3 )$; Radius: 45 
A)  Center: $( - 2,3 )$; Radius: $3 \sqrt { 5 }$ 
B)  Center: $( - 2,3 )$; Radius: 45 
C)  Center: $( 2 , - 3 )$; Radius: $3 \sqrt { 5 }$ 
D)  Center: $( 2 , - 3 )$; Radius: 45

Question 18

Use translations to graph the given function.
-$$g ( x ) = \frac { 1 } { x - 1 } + 3$$

Accepted Answer

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

Question 19

Solve the problem.
-Write an equation of the circle that is tangent to both axes with radius $\sqrt { 3 }$ and center in Quadrant IV.

Accepted Answer

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

Question 20

Choose the one alternative that best completes the statement or answers the question.
Find (f + g)(x) and identify the graph of f + g.
-$f ( x ) = x ^ { 2 }$ and $g ( x ) = 1$

Accepted Answer

A)  $( f + g ) ( x ) = x ^ { 2 } + 1$
  
B)  $( f + g ) ( x ) = ( x + 1 ) ^ { 2 }$
  
C)  $( f + g ) ( x ) = x ^ { 2 } + 1$
  
D)  $( f + g ) ( x ) = ( x + 1 ) ^ { 2 }$
  
A)  $( f + g ) ( x ) = x ^ { 2 } + 1$
  
B)  $( f + g ) ( x ) = ( x + 1 ) ^ { 2 }$
  
C)  $( f + g ) ( x ) = x ^ { 2 } + 1$
  
D)  $( f + g ) ( x ) = ( x + 1 ) ^ { 2 }$

Determine the x- and y-intercepts for the given function. - $g ( x ) = - 7 x - 15$

Solve the problem. -The fixed and variable costs to produce an item are given along with the price at which an item is sold. Determine the break-even point. Fixed cost: $\$ 2,093$ Variable cost per items: $\$ 34.50$ Price at which the item is sold: $\$ 80.00$

Write an equation of the line satisfying the given conditions. -Passes through (1, 4) and is parallel to the y-axis.

Find the indicated function and write its domain in interval notation. - $s ( x ) = \frac { x - 2 } { x ^ { 2 } - 64 } , t ( x ) = \sqrt { x + 8 } , ( s \cdot t ) ( x ) = ?$

Evaluate the function for the given value of x. - $p ( x ) = x ^ { 2 } + 7 x , q ( x ) = \sqrt { x + 3 } , ( p \cdot q ) ( x ) = ?$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Explain what it means for a relation to define y as a function of x.

Use transformations to graph the given function. - $q ( x ) = \sqrt { 5 x }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If two nonvertical lines have the same slope but different y-intercepts, then the lines are (parallel/perpendicular).

Write the equation in slope-intercept form. Then, graph the line using the slope and y-intercept. - $-5 x-2 y=0$

Determine the domain and range of the function. -

The slope of a line is given. Find the slope of a line parallel to the given line. - $m = \frac { 11 } { 10 }$

Find the midpoint of the line segment whose endpoints are the given points. - $( 3,1 )$ and $( 9,4 )$

Use transformations on the basic functions to write a rule y = f (x) that would produce the given graph. -

The distance between two distinct points ( $\left( x _ { 1 } , y _ { 1 } \right) \text { and } \left( x _ { 2 } , y _ { 2 } \right)$ ) is given by the formula .

Find the exact distance between the points. -(-9, 4) and (-5, -6)

Determine the center and radius of the circle. - $( x + 2 ) ^ { 2 } + ( y - 3 ) ^ { 2 } = 45$

Use translations to graph the given function. - $g ( x ) = \frac { 1 } { x - 1 } + 3$

Solve the problem. -Write an equation of the circle that is tangent to both axes with radius $\sqrt { 3 }$ and center in Quadrant IV.

Choose the one alternative that best completes the statement or answers the question. Find (f + g)(x) and identify the graph of f + g. - $f ( x ) = x ^ { 2 }$ and $g ( x ) = 1$

Equations and Inequalities

Polynomial and Rational Functions

Exponential and Logarithmic Functions

Systems of Equations and Inequalities

Matrices and Determinants and Applications

Analytic Geometry

Sequences, Series, Induction, and Probability

Review of Prerequisites

Filters

Exam 2: Functions and Relations

Determine the x- and y-intercepts for the given function. - g(x)=−7x−15g ( x ) = - 7 x - 15g(x)=−7x−15

Solve the problem. -The fixed and variable costs to produce an item are given along with the price at which an item is sold. Determine the break-even point. Fixed cost: $2,093\$ 2,093$2,093 Variable cost per items: $34.50\$ 34.50$34.50 Price at which the item is sold: $80.00\$ 80.00$80.00