Question 1

Identify the vertex, axis of symmetry, and intercepts for the graph of the function.
-$$y = x ^ { 2 } + 8 x + 14$$

Accepted Answer

A)  Vertex at $( - 4 , - 2 )$; axis: $y = - 2 ; x$-intercepts: none; $y$-intercept: $( - 4 - \sqrt { 2 } , 0 )$ 
B)  Vertex at $( - 4 , - 2 )$; axis: $x = - 4 ; x$-intercepts: $( - 4 - \sqrt { 2 } , 0 )$ and $( - 4 + \sqrt { 2 } , 0 ) ; y$-intercept: $( 0,14 )$ 
C)  Vertex at $( 4,62 )$; axis: $x = 4 ; x$-intercepts: none; $y$-intercept: $( - 4 + \sqrt { 2 } , 0 )$ 
D)  Vertex at $( 4,62 )$; axis: $y = 62 ; x$-intercepts: $( - 4 - \sqrt { 2 } , 0 )$ and $( - 4 + \sqrt { 2 } , 0 ) ; y$-intercept: $( 0,14 )$ 
A)  Vertex at $( - 4 , - 2 )$; axis: $y = - 2 ; x$-intercepts: none; $y$-intercept: $( - 4 - \sqrt { 2 } , 0 )$ 
B)  Vertex at $( - 4 , - 2 )$; axis: $x = - 4 ; x$-intercepts: $( - 4 - \sqrt { 2 } , 0 )$ and $( - 4 + \sqrt { 2 } , 0 ) ; y$-intercept: $( 0,14 )$ 
C)  Vertex at $( 4,62 )$; axis: $x = 4 ; x$-intercepts: none; $y$-intercept: $( - 4 + \sqrt { 2 } , 0 )$ 
D)  Vertex at $( 4,62 )$; axis: $y = 62 ; x$-intercepts: $( - 4 - \sqrt { 2 } , 0 )$ and $( - 4 + \sqrt { 2 } , 0 ) ; y$-intercept: $( 0,14 )$

Question 2

Choose the one alternative that best completes the statement or answers the question.
Write the domain in interval notation.
-$$f ( x ) = \frac { 16 x } { x ^ { 2 } + 100 }$$

Accepted Answer

A)  $( - \infty , - 10 ) \cup ( - 10,10 ) \cup ( 10 , \infty )$ 
B)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $( - \infty , 10 ) \cup ( 10 , \infty )$ 
A)  $( - \infty , - 10 ) \cup ( - 10,10 ) \cup ( 10 , \infty )$ 
B)  $( - \infty , 0 ) \cup ( 0 , \infty )$ 
C)  $( - \infty , \infty )$ 
D)  $( - \infty , 10 ) \cup ( 10 , \infty )$

Question 3

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-Given the function defined by $g ( x ) = - 3 ( x - 1 ) ^ { 3 } ( x + 5 ) ^ { 4 }$ , the value 1 is a zero with multiplicity
, and the value -5 is a zero with multiplicity .

Accepted Answer

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

Question 4

Solve the inequality. Write the solution set in interval notation.
-$$a ^ { 2 } + 6 a + 9 > 0$$

Accepted Answer

A)  $( - \infty , 3 ) \cup ( 3 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $( - \infty , - 3 ) \cup ( 3 , \infty )$ 
D)  $( - \infty , - 3 ) \cup ( - 3 , \infty )$ 
A)  $( - \infty , 3 ) \cup ( 3 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $( - \infty , - 3 ) \cup ( 3 , \infty )$ 
D)  $( - \infty , - 3 ) \cup ( - 3 , \infty )$

Question 5

Identify the asymptotes.
-$$f ( x ) = \frac { x ^ { 3 } - 4 x ^ { 2 } - 9 x + 8 } { x ^ { 2 } - 6 }$$

Accepted Answer

A)  Vertical asymptotes: $x = \sqrt { 6 }$ and $x = - \sqrt { 6 }$
Slant asymptote: $y = x - 4$ 
B)  Vertical asymptotes: $x = \sqrt { 6 }$ and $x = - \sqrt { 6 }$
Slant asymptote: $y = - 3 x - 16$ 
C)  Vertical asymptotes: $x = \sqrt { 6 }$ and $x = - \sqrt { 6 }$
Horizontal asymptote: $y = 1$ 
D)  Vertical asymptotes: $x = 6$ and $x = - 6$
Horizontal asymptote: $y = 1$ 
A)  Vertical asymptotes: $x = \sqrt { 6 }$ and $x = - \sqrt { 6 }$
Slant asymptote: $y = x - 4$ 
B)  Vertical asymptotes: $x = \sqrt { 6 }$ and $x = - \sqrt { 6 }$
Slant asymptote: $y = - 3 x - 16$ 
C)  Vertical asymptotes: $x = \sqrt { 6 }$ and $x = - \sqrt { 6 }$
Horizontal asymptote: $y = 1$ 
D)  Vertical asymptotes: $x = 6$ and $x = - 6$
Horizontal asymptote: $y = 1$

Question 6

Choose the one alternative that best completes the statement or answers the question.
Use long division to divide.
-$$\left( 3 x ^ { 3 } - 4 x ^ { 2 } + 8 \right) \div ( 2 x - 1 )$$

Accepted Answer

A)  $\frac { 3 } { 2 } x ^ { 2 } + \frac { 5 } { 4 } x + \frac { 5 } { 8 } + \frac { 8 } { 2 x - 1 }$ 
B)  $\frac { 3 } { 2 } x ^ { 2 } - 2 x - 1$ 
C)  $\frac { 3 } { 2 } x ^ { 2 } + 2 x - 1$ 
D)  $\frac { 3 } { 2 } x ^ { 2 } - \frac { 5 } { 4 } x - \frac { 5 } { 8 } + \frac { \frac { 59 } { 8 } } { 2 x - 1 }$ 
A)  $\frac { 3 } { 2 } x ^ { 2 } + \frac { 5 } { 4 } x + \frac { 5 } { 8 } + \frac { 8 } { 2 x - 1 }$ 
B)  $\frac { 3 } { 2 } x ^ { 2 } - 2 x - 1$ 
C)  $\frac { 3 } { 2 } x ^ { 2 } + 2 x - 1$ 
D)  $\frac { 3 } { 2 } x ^ { 2 } - \frac { 5 } { 4 } x - \frac { 5 } { 8 } + \frac { \frac { 59 } { 8 } } { 2 x - 1 }$

Question 7

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-If (x + 3) is a factor of a polynomial, then 3 is a zero of the polynomial.

Accepted Answer

A) True 
 B)False

Question 8

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-An even function is symmetric with respect to the axis.

Accepted Answer

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

Question 9

Choose the one alternative that best completes the statement or answers the question.
Use long division to divide.
-$\frac { 12 x ^ { 4 } - 6 x ^ { 3 } + 25 x ^ { 2 } - 11 x - 6 } { 4 x ^ { 2 } - 2 x - 1 }$

Accepted Answer

A)  $3 x ^ { 2 } + 10 x + 1$ 
B)  $3 x ^ { 2 } + 7 + \frac { 3 x + 1 } { 4 x ^ { 2 } - 2 x - 1 }$ 
C)  $3 x ^ { 2 } + 3 x + 8$ 
D)  $3 x ^ { 2 } + 7 x + \frac { 3 x + 1 } { 4 x ^ { 2 } - 2 x - 1 }$ 
A)  $3 x ^ { 2 } + 10 x + 1$ 
B)  $3 x ^ { 2 } + 7 + \frac { 3 x + 1 } { 4 x ^ { 2 } - 2 x - 1 }$ 
C)  $3 x ^ { 2 } + 3 x + 8$ 
D)  $3 x ^ { 2 } + 7 x + \frac { 3 x + 1 } { 4 x ^ { 2 } - 2 x - 1 }$

Question 10

Determine whether the intermediate value theorem guarantees that the function has a zero on the given
interval.
-$$f ( x ) = x ^ { 3 } - 8 x ^ { 2 } + 14 x + 9 ; [ 1,2 ]$$

Accepted Answer

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

Question 11

The vertical line drawn through the vertex of a quadratic function is called the of________symmetry.

Accepted Answer

The answer of The vertical line drawn through the vertex...

Question 12

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

downward;

Question 13

Refer to the graph of the function and complete the statements.
-The graph is decreasing over the interval ـــــــــــــ
The graph is increasing over the intervalـــــــــــــــــــــــ

Accepted Answer

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

Question 14

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-A quadratic function is a polynomial function of degree .

Accepted Answer

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

Question 15

Identify the graph of the function.
-$$h ( x ) = ( x + 1 ) ^ { 2 } - 2$$

Accepted Answer

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

Question 16

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-What is the leading term of $f ( x ) = - 0.6 x ^ { 2 } ( 10 x + 1 ) ^ { 3 } ( x - 1 ) ^ { 4 }$ ?

Accepted Answer

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

Question 17

Graph the function.
-$$f ( x ) = \frac { x - 2 } { x - 3 }$$

Accepted Answer

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

Question 18

Graph the function.
-$$f ( x ) = \frac { 5 } { 3 x + 8 }$$

Accepted Answer

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

Question 19

Solve the inequality. Write the solution set in interval notation.
-$$- 16 y - 64 \geq y ^ { 2 }$$

Accepted Answer

A)  $\{ - 8 \}$ 
B)  \{ \} 
C)  $( - \infty , - 8 ) \cup ( - 8 , \infty )$ 
D)  $( - \infty , \infty )$ 
A)  $\{ - 8 \}$ 
B)  \{ \} 
C)  $( - \infty , - 8 ) \cup ( - 8 , \infty )$ 
D)  $( - \infty , \infty )$

Question 20

Write a polynomial f (x) that meets the given conditions. Answers may vary.
-Degree 2 polynomial with zeros $3 \sqrt { 5 }$ and $- 3 \sqrt { 5 }$

Accepted Answer

A)  $f ( x ) = x ^ { 2 } - 6 \sqrt { 5 } x + 45$ 
B)  $f ( x ) = x ^ { 2 } + 45$ 
C)  $f ( x ) = x ^ { 2 } + 6 \sqrt { 5 } x + 45$ 
D)  $f ( x ) = x ^ { 2 } - 45$ 
A)  $f ( x ) = x ^ { 2 } - 6 \sqrt { 5 } x + 45$ 
B)  $f ( x ) = x ^ { 2 } + 45$ 
C)  $f ( x ) = x ^ { 2 } + 6 \sqrt { 5 } x + 45$ 
D)  $f ( x ) = x ^ { 2 } - 45$

Identify the vertex, axis of symmetry, and intercepts for the graph of the function. - $y = x ^ { 2 } + 8 x + 14$

Choose the one alternative that best completes the statement or answers the question. Write the domain in interval notation. - $f ( x ) = \frac { 16 x } { x ^ { 2 } + 100 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given the function defined by $g ( x ) = - 3 ( x - 1 ) ^ { 3 } ( x + 5 ) ^ { 4 }$ , the value 1 is a zero with multiplicity , and the value -5 is a zero with multiplicity .

Solve the inequality. Write the solution set in interval notation. - $a ^ { 2 } + 6 a + 9 > 0$

Identify the asymptotes. - $f ( x ) = \frac { x ^ { 3 } - 4 x ^ { 2 } - 9 x + 8 } { x ^ { 2 } - 6 }$

Choose the one alternative that best completes the statement or answers the question. Use long division to divide. - $\left( 3 x ^ { 3 } - 4 x ^ { 2 } + 8 \right) \div ( 2 x - 1 )$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If (x + 3) is a factor of a polynomial, then 3 is a zero of the polynomial.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An even function is symmetric with respect to the axis.

Choose the one alternative that best completes the statement or answers the question. Use long division to divide. - $\frac { 12 x ^ { 4 } - 6 x ^ { 3 } + 25 x ^ { 2 } - 11 x - 6 } { 4 x ^ { 2 } - 2 x - 1 }$

Determine whether the intermediate value theorem guarantees that the function has a zero on the given interval. - $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } + 14 x + 9 ; [ 1,2 ]$

The vertical line drawn through the vertex of a quadratic function is called the of________symmetry.

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

Refer to the graph of the function and complete the statements. -The graph is decreasing over the interval ـــــــــــــ The graph is increasing over the intervalـــــــــــــــــــــــ

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A quadratic function is a polynomial function of degree .

Identify the graph of the function. - $h ( x ) = ( x + 1 ) ^ { 2 } - 2$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -What is the leading term of $f ( x ) = - 0.6 x ^ { 2 } ( 10 x + 1 ) ^ { 3 } ( x - 1 ) ^ { 4 }$ ?

Graph the function. - $f ( x ) = \frac { x - 2 } { x - 3 }$

Graph the function. - $f ( x ) = \frac { 5 } { 3 x + 8 }$

Solve the inequality. Write the solution set in interval notation. - $- 16 y - 64 \geq y ^ { 2 }$

Write a polynomial f (x) that meets the given conditions. Answers may vary. -Degree 2 polynomial with zeros $3 \sqrt { 5 }$ and $- 3 \sqrt { 5 }$

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

Identify the vertex, axis of symmetry, and intercepts for the graph of the function. - y=x2+8x+14y = x ^ { 2 } + 8 x + 14y=x2+8x+14

Choose the one alternative that best completes the statement or answers the question. Write the domain in interval notation. - f(x)=16xx2+100f ( x ) = \frac { 16 x } { x ^ { 2 } + 100 }f(x)=x2+10016x​

Solve the inequality. Write the solution set in interval notation. - a2+6a+9>0a ^ { 2 } + 6 a + 9 > 0a2+6a+9>0

Identify the asymptotes. - f(x)=x3−4x2−9x+8x2−6f ( x ) = \frac { x ^ { 3 } - 4 x ^ { 2 } - 9 x + 8 } { x ^ { 2 } - 6 }f(x)=x2−6x3−4x2−9x+8​

Choose the one alternative that best completes the statement or answers the question. Use long division to divide. - (3x3−4x2+8)÷(2x−1)\left( 3 x ^ { 3 } - 4 x ^ { 2 } + 8 \right) \div ( 2 x - 1 )(3x3−4x2+8)÷(2x−1)

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -If (x + 3) is a factor of a polynomial, then 3 is a zero of the polynomial.

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -An even function is symmetric with respect to the axis.

Choose the one alternative that best completes the statement or answers the question. Use long division to divide. - 12x4−6x3+25x2−11x−64x2−2x−1\frac { 12 x ^ { 4 } - 6 x ^ { 3 } + 25 x ^ { 2 } - 11 x - 6 } { 4 x ^ { 2 } - 2 x - 1 }4x2−2x−112x4−6x3+25x2−11x−6​

Determine whether the intermediate value theorem guarantees that the function has a zero on the given interval. - f(x)=x3−8x2+14x+9;[1,2]f ( x ) = x ^ { 3 } - 8 x ^ { 2 } + 14 x + 9 ; [ 1,2 ]f(x)=x3−8x2+14x+9;[1,2]

The vertical line drawn through the vertex of a quadratic function is called the of________symmetry.

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________ .

Refer to the graph of the function and complete the statements. -The graph is decreasing over the interval ـــــــــــــ The graph is increasing over the intervalـــــــــــــــــــــــ

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A quadratic function is a polynomial function of degree .

Identify the graph of the function. - h(x)=(x+1)2−2h ( x ) = ( x + 1 ) ^ { 2 } - 2h(x)=(x+1)2−2

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -What is the leading term of f(x)=−0.6x2(10x+1)3(x−1)4f ( x ) = - 0.6 x ^ { 2 } ( 10 x + 1 ) ^ { 3 } ( x - 1 ) ^ { 4 }f(x)=−0.6x2(10x+1)3(x−1)4 ?

Graph the function. - f(x)=x−2x−3f ( x ) = \frac { x - 2 } { x - 3 }f(x)=x−3x−2​

Graph the function. - f(x)=53x+8f ( x ) = \frac { 5 } { 3 x + 8 }f(x)=3x+85​

Solve the inequality. Write the solution set in interval notation. - −16y−64≥y2- 16 y - 64 \geq y ^ { 2 }−16y−64≥y2

Write a polynomial f (x) that meets the given conditions. Answers may vary. -Degree 2 polynomial with zeros 353 \sqrt { 5 }35​ and −35- 3 \sqrt { 5 }−35​

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

Identify the vertex, axis of symmetry, and intercepts for the graph of the function. - $y = x ^ { 2 } + 8 x + 14$

Choose the one alternative that best completes the statement or answers the question. Write the domain in interval notation. - $f ( x ) = \frac { 16 x } { x ^ { 2 } + 100 }$

Solve the inequality. Write the solution set in interval notation. - $a ^ { 2 } + 6 a + 9 > 0$

Identify the asymptotes. - $f ( x ) = \frac { x ^ { 3 } - 4 x ^ { 2 } - 9 x + 8 } { x ^ { 2 } - 6 }$

Choose the one alternative that best completes the statement or answers the question. Use long division to divide. - $\left( 3 x ^ { 3 } - 4 x ^ { 2 } + 8 \right) \div ( 2 x - 1 )$

Choose the one alternative that best completes the statement or answers the question. Use long division to divide. - $\frac { 12 x ^ { 4 } - 6 x ^ { 3 } + 25 x ^ { 2 } - 11 x - 6 } { 4 x ^ { 2 } - 2 x - 1 }$

Determine whether the intermediate value theorem guarantees that the function has a zero on the given interval. - $f ( x ) = x ^ { 3 } - 8 x ^ { 2 } + 14 x + 9 ; [ 1,2 ]$

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

Identify the graph of the function. - $h ( x ) = ( x + 1 ) ^ { 2 } - 2$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -What is the leading term of $f ( x ) = - 0.6 x ^ { 2 } ( 10 x + 1 ) ^ { 3 } ( x - 1 ) ^ { 4 }$ ?

Graph the function. - $f ( x ) = \frac { x - 2 } { x - 3 }$

Graph the function. - $f ( x ) = \frac { 5 } { 3 x + 8 }$

Solve the inequality. Write the solution set in interval notation. - $- 16 y - 64 \geq y ^ { 2 }$

Write a polynomial f (x) that meets the given conditions. Answers may vary. -Degree 2 polynomial with zeros $3 \sqrt { 5 }$ and $- 3 \sqrt { 5 }$