Question 1

Solve the inequality. Write the solution set in interval notation.
-$$4 x ^ { 2 } - 19 x - 30 \geq 0$$

Accepted Answer

A)  $( - \infty , - 6 ] \cup \left[ \frac { 5 } { 4 } , \infty \right)$ 
B)  $\left[ - 6 , \frac { 5 } { 4 } \right]$ 
C)  $\left[ - \frac { 5 } { 4 } , 6 \right]$ 
D)  $\left[ - \infty , - \frac { 5 } { 4 } \right] \cup [ 6 , \infty )$ 
A)  $( - \infty , - 6 ] \cup \left[ \frac { 5 } { 4 } , \infty \right)$ 
B)  $\left[ - 6 , \frac { 5 } { 4 } \right]$ 
C)  $\left[ - \frac { 5 } { 4 } , 6 \right]$ 
D)  $\left[ - \infty , - \frac { 5 } { 4 } \right] \cup [ 6 , \infty )$

Question 2

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-$$\text { Given } \frac { 2 x ^ { 3 } - 5 x ^ { 2 } - 6 x + 1 } { x - 3 } = 2 x ^ { 2 } + x - 3 + \frac { - 8 } { x - 3 } \text {, use the division algorithm to check the result. }$$

Accepted Answer

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

Question 3

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-Given $f ( x ) = \frac { 2 x ^ { 3 } + 7 } { 5 x ^ { 3 } }$, the graph of $f$ will behave like the graph of which of the following functions for large values of $| x |$ ?

Accepted Answer

A)  $y = \frac { 2 } { 5 x }$ 
B)  $y = \frac { 2 x } { 5 }$ 
C)  $y = \frac { 2 } { 5 }$ 
D)  $\mathrm { y } = \frac { 2 } { 5 } x ^ { 3 }$ 
A)  $y = \frac { 2 } { 5 x }$ 
B)  $y = \frac { 2 x } { 5 }$ 
C)  $y = \frac { 2 } { 5 }$ 
D)  $\mathrm { y } = \frac { 2 } { 5 } x ^ { 3 }$

Question 4

Use synthetic division to divide the polynomials.
-$$\left( - 3 x ^ { 4 } - 10 x ^ { 3 } + 38 x ^ { 2 } + 58 x - 52 \right) \div \left( x - \frac { 2 } { 3 } \right)$$

Accepted Answer

A)  $- x ^ { 3 } + 4 x ^ { 2 } - 10 x - 26$ 
B)  $- 3 x ^ { 3 } + 12 x ^ { 2 } - 30 x - 78$ 
C)  $- 3 x ^ { 3 } - 12 x ^ { 2 } + 30 x + 78$ 
D)  $- 3 x ^ { 3 } - 4 x ^ { 2 } + 10 x - 26$ 
A)  $- x ^ { 3 } + 4 x ^ { 2 } - 10 x - 26$ 
B)  $- 3 x ^ { 3 } + 12 x ^ { 2 } - 30 x - 78$ 
C)  $- 3 x ^ { 3 } - 12 x ^ { 2 } + 30 x + 78$ 
D)  $- 3 x ^ { 3 } - 4 x ^ { 2 } + 10 x - 26$

Question 5

Use synthetic division to divide the polynomials.
-$$\left( s ^ { 2 } + 2 s - 8 \right) \div ( s + 4 )$$

Accepted Answer

A)  $s + 2 - \frac { 4 } { s + 4 }$ 
B)  $s + 2$ 
C)  $s + 2 + \frac { 4 } { s + 4 }$ 
D)  $s - 2$ 
A)  $s + 2 - \frac { 4 } { s + 4 }$ 
B)  $s + 2$ 
C)  $s + 2 + \frac { 4 } { s + 4 }$ 
D)  $s - 2$

Question 6

Identify the vertex and sketch the graph.
-$$f ( x ) = - 2 x ^ { 2 } - 24 x - 72$$

Accepted Answer

A) 
11ecc2e0_952d_9d33_8
Vertex: $( 6,0 )$ 
B) 
 
Vertex: $( - 6,0 )$ 
C) 
 
Vertex: $( - 6,0 )$ 
D) 
 
Vertex: $( 6,0 )$ 
A) 
11ecc2e0_952d_9d33_8
Vertex: $( 6,0 )$ 
B) 
 
Vertex: $( - 6,0 )$ 
C) 
 
Vertex: $( - 6,0 )$ 
D) 
 
Vertex: $( 6,0 )$

Question 7

Refer to the graph of the function and complete the statements.
-The graph is increasing over the interval(s) ــــــــــــــــــــ
The graph is decreasing over the interval(s)ــــــــــــــــــــــــ

Accepted Answer

A)  Never increasing;
$( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
B)  $( - \infty , 3 ) \cup ( 3 , \infty )$;
Never decreasing 
C)  Never increasing;
$( - \infty , 3 ) \cup ( 3 , \infty )$ 
D)  $( - \infty , - 3 ) \cup ( - 3 , \infty )$;
Never decreasing 
A)  Never increasing;
$( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
B)  $( - \infty , 3 ) \cup ( 3 , \infty )$;
Never decreasing 
C)  Never increasing;
$( - \infty , 3 ) \cup ( 3 , \infty )$ 
D)  $( - \infty , - 3 ) \cup ( - 3 , \infty )$;
Never decreasing

Question 8

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-If the leading term of a polynomial function is $a x ^ { n }$ where a is negative and n is odd, determine the
end behavior.

Accepted Answer

up to the

Question 9

Determine the minimum or maximum value of the function.
-$$k ( x ) = 3 x ^ { 2 } - 4 x$$

Accepted Answer

A)  Minimum: $\frac { 4 } { 3 }$ 
B)  Minimum: $- \frac { 4 } { 3 }$ 
C)  Maximum: $- \frac { 4 } { 3 }$ 
D)  Maximum: $\frac { 4 } { 3 }$ 
A)  Minimum: $\frac { 4 } { 3 }$ 
B)  Minimum: $- \frac { 4 } { 3 }$ 
C)  Maximum: $- \frac { 4 } { 3 }$ 
D)  Maximum: $\frac { 4 } { 3 }$

Question 10

Write the domain and range of the function in interval notation.
-$$q ( x ) = 2 x ^ { 2 } - 12 x + 2$$

Accepted Answer

A)  Domain: $( - \infty , \infty )$
Range: $( - \infty , - 16 ]$ 
B)  Domain: $[ - 16 , \infty )$
Range: $( - \infty , \infty )$ 
C)  Domain: $( - \infty , \infty )$
Range: $[ - 16 , \infty )$ 
D)  Domain : $[ 0 , \infty )$
Range: $( \infty , \infty )$ 
A)  Domain: $( - \infty , \infty )$
Range: $( - \infty , - 16 ]$ 
B)  Domain: $[ - 16 , \infty )$
Range: $( - \infty , \infty )$ 
C)  Domain: $( - \infty , \infty )$
Range: $[ - 16 , \infty )$ 
D)  Domain : $[ 0 , \infty )$
Range: $( \infty , \infty )$

Question 11

Graph the function.
-$$g ( x ) = \frac { x ^ { 3 } + 5 x ^ { 2 } - 4 x - 20 } { x ^ { 2 } + 3 x }$$

Accepted Answer

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

Question 12

Solve the problem.
-A power company burns coal to generate electricity. The cost C x (in $1000) to remove x% of the air pollutants is given by: $C ( x ) = \frac { 500 x } { 140 - x }$ 
a. Compute the cost to remove 25% of the air pollutants.
b. If the power company budgets $1.4 million for pollution control, what percentage of the air Pollutants can be removed?

Accepted Answer

A)  a. $\frac { 2500000 } { 23 }$
b. $135.17 \%$ 
B)  a. $\frac { 2500 } { 23 }$
b. $135.17 \%$ 
C)  a. $\frac { 2500 } { 23 }$
b. $103.16 \%$ 
D)  a. $\frac { 2500000 } { 23 }$
b. $103.16 \%$ 
A)  a. $\frac { 2500000 } { 23 }$
b. $135.17 \%$ 
B)  a. $\frac { 2500 } { 23 }$
b. $135.17 \%$ 
C)  a. $\frac { 2500 } { 23 }$
b. $103.16 \%$ 
D)  a. $\frac { 2500000 } { 23 }$
b. $103.16 \%$

Question 13

Graph the function by using transformations of the graph of $y = \frac { 1 } { x ^ { 2 } }$
-$$f ( x ) = \frac { 1 } { ( x - 1 ) ^ { 2 } } - 2$$

Accepted Answer

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

Question 14

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The notation $x \rightarrow 5 ^ { - }$ is read as .

Accepted Answer

x approach

Question 15

Find the vertex.
-$$f ( x ) = - 2 ( x - 19 ) ^ { 2 } + 13$$

Accepted Answer

A)  $( 13 , - 19 )$ 
B)  $( 13,19 )$ 
C)  $( - 19,13 )$ 
D)  $( 19,13 )$ 
A)  $( 13 , - 19 )$ 
B)  $( 13,19 )$ 
C)  $( - 19,13 )$ 
D)  $( 19,13 )$

Question 16

Use the factor theorem to determine if the given binomial is a factor of f (x).
-$$f ( x ) = 2 x ^ { 3 } + x ^ { 2 } - 9 x - 6 ; x - 1$$

Accepted Answer

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

Question 17

Find all the zeros.
-$$f ( x ) = x ^ { 3 } + 10 x ^ { 2 } + 25 x + 18$$

Accepted Answer

A)  $2 , - 4 \pm 7 i$ 
B)  $- 2 , - 4 \pm 7 i$ 
C)  $- 2 , - 4 \pm \sqrt { 7 }$ 
D)  $2 , - 4 \pm \sqrt { 7 }$ 
A)  $2 , - 4 \pm 7 i$ 
B)  $- 2 , - 4 \pm 7 i$ 
C)  $- 2 , - 4 \pm \sqrt { 7 }$ 
D)  $2 , - 4 \pm \sqrt { 7 }$

Question 18

Given $f ( x ) = a ( x - h ) ^ { 2 } + k , \text { if } a < 0$ e parabola opened (upward/downward) and the (minimum/maximum) value is ________.

Accepted Answer

The answer of Given \(f ( x ) = a...

Question 19

Solve the problem.
-$$f ( x ) = - \frac { 1 } { 8 } ( x - 1 ) ^ { 4 }$$
a. Identify the power function of the form $y = x ^ { n }$ that is the parent function to the given graph.
b. In order, outline the transformations that would be required on the graph of $y = x ^ { n }$ to make the graph of the given function.
c. Match the function with the graph.
i.

ii.

iii.

iv.

Accepted Answer

A)  a. $y = x ^ { 4 }$
b. Shift $y = x ^ { 4 }$ to the right 1 units. Shrink vertically by a factor of $\frac { 1 } { 8 }$. Reflect across the $x$-axis.
c. Graph iii. 
B)  a. $y = x ^ { 4 }$
b. Shift $y = x ^ { 4 }$ to the left 1 units. Shrink vertically by a factor of $\frac { 1 } { 4 }$. Reflect across the $x$-axis.
c. Graph iii. 
C)  a. $y = x ^ { 4 }$
b. Shift $y = x ^ { 4 }$ to the right 1 units. Shrink vertically by a factor of $\frac { 1 } { 8 }$. Reflect across the $x$-axis.
c. Graph ii. 
D)  a. $y = x ^ { 4 }$
b. Shift $y = x ^ { 4 }$ to the left 1 units. Shrink vertically by a factor of $\frac { 1 } { 4 }$.
c. Graph i. 
A)  a. $y = x ^ { 4 }$
b. Shift $y = x ^ { 4 }$ to the right 1 units. Shrink vertically by a factor of $\frac { 1 } { 8 }$. Reflect across the $x$-axis.
c. Graph iii. 
B)  a. $y = x ^ { 4 }$
b. Shift $y = x ^ { 4 }$ to the left 1 units. Shrink vertically by a factor of $\frac { 1 } { 4 }$. Reflect across the $x$-axis.
c. Graph iii. 
C)  a. $y = x ^ { 4 }$
b. Shift $y = x ^ { 4 }$ to the right 1 units. Shrink vertically by a factor of $\frac { 1 } { 8 }$. Reflect across the $x$-axis.
c. Graph ii. 
D)  a. $y = x ^ { 4 }$
b. Shift $y = x ^ { 4 }$ to the left 1 units. Shrink vertically by a factor of $\frac { 1 } { 4 }$.
c. Graph i.

Question 20

Choose the one alternative that best completes the statement or answers the question.
Write a variation model using k as the constant of variation.
-The variable v varies jointly as w and x and inversely as the fourth root of y.

Accepted Answer

A)  $v = w x \frac { \sqrt [ 4 ] { y } } { k }$ 
B)  $v = \sqrt [ 4 ] { \frac { k w x } { y } }$ 
C)  $v = \frac { k w x } { \sqrt [ 4 ] { y } }$ 
D)  $v = w x _ { \sqrt [ 4 ] { \frac { y } { k } } } ^ { \sqrt { \frac { y } { k } } }$ 
A)  $v = w x \frac { \sqrt [ 4 ] { y } } { k }$ 
B)  $v = \sqrt [ 4 ] { \frac { k w x } { y } }$ 
C)  $v = \frac { k w x } { \sqrt [ 4 ] { y } }$ 
D)  $v = w x _ { \sqrt [ 4 ] { \frac { y } { k } } } ^ { \sqrt { \frac { y } { k } } }$

Solve the inequality. Write the solution set in interval notation. - $4 x ^ { 2 } - 19 x - 30 \geq 0$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. - $\text { Given } \frac { 2 x ^ { 3 } - 5 x ^ { 2 } - 6 x + 1 } { x - 3 } = 2 x ^ { 2 } + x - 3 + \frac { - 8 } { x - 3 } \text {, use the division algorithm to check the result. }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given $f ( x ) = \frac { 2 x ^ { 3 } + 7 } { 5 x ^ { 3 } }$ , the graph of $f$ will behave like the graph of which of the following functions for large values of $| x |$ ?

Use synthetic division to divide the polynomials. - $\left( - 3 x ^ { 4 } - 10 x ^ { 3 } + 38 x ^ { 2 } + 58 x - 52 \right) \div \left( x - \frac { 2 } { 3 } \right)$

Use synthetic division to divide the polynomials. - $\left( s ^ { 2 } + 2 s - 8 \right) \div ( s + 4 )$

Identify the vertex and sketch the graph. - $f ( x ) = - 2 x ^ { 2 } - 24 x - 72$

Refer to the graph of the function and complete the statements. -The graph is increasing over the interval(s) ــــــــــــــــــــ The graph is decreasing over the interval(s)ــــــــــــــــــــــــ

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If the leading term of a polynomial function is $a x ^ { n }$ where a is negative and n is odd, determine the end behavior.

Determine the minimum or maximum value of the function. - $k ( x ) = 3 x ^ { 2 } - 4 x$

Write the domain and range of the function in interval notation. - $q ( x ) = 2 x ^ { 2 } - 12 x + 2$

Graph the function. - $g ( x ) = \frac { x ^ { 3 } + 5 x ^ { 2 } - 4 x - 20 } { x ^ { 2 } + 3 x }$

Graph the function by using transformations of the graph of $y = \frac { 1 } { x ^ { 2 } }$ - $f ( x ) = \frac { 1 } { ( x - 1 ) ^ { 2 } } - 2$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The notation $x \rightarrow 5 ^ { - }$ is read as .

Find the vertex. - $f ( x ) = - 2 ( x - 19 ) ^ { 2 } + 13$

Use the factor theorem to determine if the given binomial is a factor of f (x). - $f ( x ) = 2 x ^ { 3 } + x ^ { 2 } - 9 x - 6 ; x - 1$

Find all the zeros. - $f ( x ) = x ^ { 3 } + 10 x ^ { 2 } + 25 x + 18$

Given $f ( x ) = a ( x - h ) ^ { 2 } + k , \text { if } a < 0$ e parabola opened (upward/downward) and the (minimum/maximum) value is ________.

Choose the one alternative that best completes the statement or answers the question. Write a variation model using k as the constant of variation. -The variable v varies jointly as w and x and inversely as the fourth root of y.

Equations and Inequalities

Functions and Relations

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 3: Polynomial and Rational Functions

Solve the inequality. Write the solution set in interval notation. - 4x2−19x−30≥04 x ^ { 2 } - 19 x - 30 \geq 04x2−19x−30≥0

Use synthetic division to divide the polynomials. - (−3x4−10x3+38x2+58x−52)÷(x−23)\left( - 3 x ^ { 4 } - 10 x ^ { 3 } + 38 x ^ { 2 } + 58 x - 52 \right) \div \left( x - \frac { 2 } { 3 } \right)(−3x4−10x3+38x2+58x−52)÷(x−32​)

Use synthetic division to divide the polynomials. - (s2+2s−8)÷(s+4)\left( s ^ { 2 } + 2 s - 8 \right) \div ( s + 4 )(s2+2s−8)÷(s+4)

Identify the vertex and sketch the graph. - f(x)=−2x2−24x−72f ( x ) = - 2 x ^ { 2 } - 24 x - 72f(x)=−2x2−24x−72

Refer to the graph of the function and complete the statements. -The graph is increasing over the interval(s) ــــــــــــــــــــ The graph is decreasing over the interval(s)ــــــــــــــــــــــــ

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If the leading term of a polynomial function is axna x ^ { n }axn where a is negative and n is odd, determine the end behavior.

Determine the minimum or maximum value of the function. - k(x)=3x2−4xk ( x ) = 3 x ^ { 2 } - 4 xk(x)=3x2−4x

Write the domain and range of the function in interval notation. - q(x)=2x2−12x+2q ( x ) = 2 x ^ { 2 } - 12 x + 2q(x)=2x2−12x+2

Graph the function. - g(x)=x3+5x2−4x−20x2+3xg ( x ) = \frac { x ^ { 3 } + 5 x ^ { 2 } - 4 x - 20 } { x ^ { 2 } + 3 x }g(x)=x2+3xx3+5x2−4x−20​

Graph the function by using transformations of the graph of y=1x2y = \frac { 1 } { x ^ { 2 } }y=x21​ - f(x)=1(x−1)2−2f ( x ) = \frac { 1 } { ( x - 1 ) ^ { 2 } } - 2f(x)=(x−1)21​−2

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The notation x→5−x \rightarrow 5 ^ { - }x→5− is read as .

Find the vertex. - f(x)=−2(x−19)2+13f ( x ) = - 2 ( x - 19 ) ^ { 2 } + 13f(x)=−2(x−19)2+13

Use the factor theorem to determine if the given binomial is a factor of f (x). - f(x)=2x3+x2−9x−6;x−1f ( x ) = 2 x ^ { 3 } + x ^ { 2 } - 9 x - 6 ; x - 1f(x)=2x3+x2−9x−6;x−1

Find all the zeros. - f(x)=x3+10x2+25x+18f ( x ) = x ^ { 3 } + 10 x ^ { 2 } + 25 x + 18f(x)=x3+10x2+25x+18

Given f(x)=a(x−h)2+k, if a<0f ( x ) = a ( x - h ) ^ { 2 } + k , \text { if } a < 0f(x)=a(x−h)2+k, if a<0 e parabola opened (upward/downward) and the (minimum/maximum) value is ________.

Choose the one alternative that best completes the statement or answers the question. Write a variation model using k as the constant of variation. -The variable v varies jointly as w and x and inversely as the fourth root of y.

Equations and Inequalities

Functions and Relations

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

Solve the inequality. Write the solution set in interval notation. - $4 x ^ { 2 } - 19 x - 30 \geq 0$

Use synthetic division to divide the polynomials. - $\left( - 3 x ^ { 4 } - 10 x ^ { 3 } + 38 x ^ { 2 } + 58 x - 52 \right) \div \left( x - \frac { 2 } { 3 } \right)$

Use synthetic division to divide the polynomials. - $\left( s ^ { 2 } + 2 s - 8 \right) \div ( s + 4 )$

Identify the vertex and sketch the graph. - $f ( x ) = - 2 x ^ { 2 } - 24 x - 72$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If the leading term of a polynomial function is $a x ^ { n }$ where a is negative and n is odd, determine the end behavior.

Determine the minimum or maximum value of the function. - $k ( x ) = 3 x ^ { 2 } - 4 x$

Write the domain and range of the function in interval notation. - $q ( x ) = 2 x ^ { 2 } - 12 x + 2$

Graph the function. - $g ( x ) = \frac { x ^ { 3 } + 5 x ^ { 2 } - 4 x - 20 } { x ^ { 2 } + 3 x }$

Graph the function by using transformations of the graph of $y = \frac { 1 } { x ^ { 2 } }$ - $f ( x ) = \frac { 1 } { ( x - 1 ) ^ { 2 } } - 2$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The notation $x \rightarrow 5 ^ { - }$ is read as .

Find the vertex. - $f ( x ) = - 2 ( x - 19 ) ^ { 2 } + 13$

Use the factor theorem to determine if the given binomial is a factor of f (x). - $f ( x ) = 2 x ^ { 3 } + x ^ { 2 } - 9 x - 6 ; x - 1$

Find all the zeros. - $f ( x ) = x ^ { 3 } + 10 x ^ { 2 } + 25 x + 18$

Given $f ( x ) = a ( x - h ) ^ { 2 } + k , \text { if } a < 0$ e parabola opened (upward/downward) and the (minimum/maximum) value is ________.