Question 1

Solve the inequality. Write the solution set in interval notation.
-$$\frac { 3 x - 4 } { 3 + 2 x } < 0$$

Accepted Answer

A)  $\left( - \infty , - \frac { 3 } { 2 } \right) \cup \left( \frac { 4 } { 3 } , \frac { 3 } { 2 } \right)$ 
B)  $\left( - \frac { 3 } { 2 } , \frac { 4 } { 3 } \right)$ 
C)  $\left( - \infty , - \frac { 4 } { 3 } \right) \cup \left( \frac { 3 } { 2 } , \infty \right)$ 
D)  $\left( - \frac { 4 } { 3 } , \frac { 3 } { 2 } \right)$ 
A)  $\left( - \infty , - \frac { 3 } { 2 } \right) \cup \left( \frac { 4 } { 3 } , \frac { 3 } { 2 } \right)$ 
B)  $\left( - \frac { 3 } { 2 } , \frac { 4 } { 3 } \right)$ 
C)  $\left( - \infty , - \frac { 4 } { 3 } \right) \cup \left( \frac { 3 } { 2 } , \infty \right)$ 
D)  $\left( - \frac { 4 } { 3 } , \frac { 3 } { 2 } \right)$ B

Question 2

Solve the problem.
-The following table represents the result of a synthetic division. $\begin{array} { c | c c c c } 
- 2 & - 9 & - 8 & 5 & - 8 \
& & 18 & - 20 & 30 \
\hline & - 9 & 10 & - 15 & \mid 22
\end{array}$

Use $x$ as the variable. Identify the quotient.

Accepted Answer

A)  $x + 2$ 
B)  $- 9 x ^ { 3 } - 8 x ^ { 2 } + 5 x - 8$ 
C)  $x - 2$ 
D)  $- 9 x ^ { 2 } + 10 x - 15$ 
A)  $x + 2$ 
B)  $- 9 x ^ { 3 } - 8 x ^ { 2 } + 5 x - 8$ 
C)  $x - 2$ 
D)  $- 9 x ^ { 2 } + 10 x - 15$ D

Question 3

Find the zeros of the function and state the multiplicities.
-$$f ( x ) = - 2 x ^ { 6 } ( x + 7 ) ^ { 2 } ( x - 5 ) ^ { 6 }$$

Accepted Answer

A)  $- 7$ (multiplicity 2), 5 (multiplicity 6) 
B)  7 (multiplicity 2), $- 5$ (multiplicity 6) 
C)  0 (multiplicity 6), 7 (multiplicity 2), $- 5$ (multiplicity 6) 
D)  0 (multiplicity 6), $- 7$ (multiplicity 2), 5 (multiplicity 6) 
A)  $- 7$ (multiplicity 2), 5 (multiplicity 6) 
B)  7 (multiplicity 2), $- 5$ (multiplicity 6) 
C)  0 (multiplicity 6), 7 (multiplicity 2), $- 5$ (multiplicity 6) 
D)  0 (multiplicity 6), $- 7$ (multiplicity 2), 5 (multiplicity 6) D

Question 4

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-Given a polynomial f (x), the factor theorem indicates that if f (c) = 0, then x - c is a of f
(x). Furthermore, if x - c is a factor of f (x), then f (c) = .

Accepted Answer

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

Question 5

Determine the number of possible positive and negative real zeros for the given function.
-$$f ( x ) = - 8 x ^ { 7 } - 7 x ^ { 4 } - 6 x ^ { 3 } + 4 x ^ { 2 } + 6 x + 5$$

Accepted Answer

A)  Positive: 1; Negative: 4 or 2 
B)  Positive: 4 or 2; Negative: 1 
C)  Positive: 4; Negative: 1 
D)  Positive: 1; Negative: 4 
A)  Positive: 1; Negative: 4 or 2 
B)  Positive: 4 or 2; Negative: 1 
C)  Positive: 4; Negative: 1 
D)  Positive: 1; Negative: 4

Question 6

Refer to the graph of the function and complete the statements.
-The domain isــــــــــــ
The range isــــــــــــــــ

Accepted Answer

A)  $( - \infty , \infty )$;
$( - \infty , \infty )$ 
B)  $( - 9 , \infty )$;
$( - \infty , 6 ) \cup ( 6 , \infty )$; 
C)  $( - \infty , 6 ) \cup ( 6 , \infty )$;
$( - 9 , \infty )$ 
D)  $( - \infty , \infty )$;
$( - 9 , \infty )$ 
A)  $( - \infty , \infty )$;
$( - \infty , \infty )$ 
B)  $( - 9 , \infty )$;
$( - \infty , 6 ) \cup ( 6 , \infty )$; 
C)  $( - \infty , 6 ) \cup ( 6 , \infty )$;
$( - 9 , \infty )$ 
D)  $( - \infty , \infty )$;
$( - 9 , \infty )$

Question 7

Write the domain and range of the function in interval notation.
-$$f ( x ) = x ^ { 2 } + 10 x + 6$$

Accepted Answer

A)  Domain: $( 0 , \infty )$
Range: $( - \infty , - 19 ]$ 
B)  Domain: $( - \infty , \infty )$
Range: $[ - 19 , \infty )$ 
C)  Domain: $( - \infty , \infty )$
Range: $( - \infty , 6 ]$ 
D)  Domain: $( - \infty , \infty )$
Range: $[ 6 , \infty )$ 
A)  Domain: $( 0 , \infty )$
Range: $( - \infty , - 19 ]$ 
B)  Domain: $( - \infty , \infty )$
Range: $[ - 19 , \infty )$ 
C)  Domain: $( - \infty , \infty )$
Range: $( - \infty , 6 ]$ 
D)  Domain: $( - \infty , \infty )$
Range: $[ 6 , \infty )$

Question 8

Choose the one alternative that best completes the statement or answers the question.
Use long division to divide.
-$\frac { 64 x ^ { 3 } + 1 } { 4 x + 1 }$

Accepted Answer

A)  $16 x ^ { 2 } - 4 x + 1$ 
B)  $16 x ^ { 2 } + 1$ 
C)  $16 x ^ { 2 } - 1$ 
D)  $16 x ^ { 2 } + 4 x + 1$ 
A)  $16 x ^ { 2 } - 4 x + 1$ 
B)  $16 x ^ { 2 } + 1$ 
C)  $16 x ^ { 2 } - 1$ 
D)  $16 x ^ { 2 } + 4 x + 1$

Question 9

The graph of y = f (x) is given. Solve the inequality.
-$$f ( x ) \leq 0$$

Accepted Answer

A)  { } 
B)  $\{ - 3 \}$ 
C)  $( - \infty , \infty )$ 
D)  $( - \infty , - 3 ] \cup [ - 3 , \infty )$ 
A)  { } 
B)  $\{ - 3 \}$ 
C)  $( - \infty , \infty )$ 
D)  $( - \infty , - 3 ] \cup [ - 3 , \infty )$

Question 10

Solve the inequality. Write the solution set in interval notation.
-$\frac { 40 - 8 x } { x ^ { 2 } } \leq 0$

Accepted Answer

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

Question 11

Refer to the graph of the function and complete the statements.
-As $x \rightarrow - \infty , f ( x ) \rightarrow$ــــــــــــــــــــ
As $x \rightarrow \infty , f ( x ) \rightarrow$ ــــــــــــــ

Accepted Answer

A)  $1 ; 1$ 
B)  $\infty ; \infty$ 
C)  $- \infty ; \infty$ 
D)  5,5 
A)  $1 ; 1$ 
B)  $\infty ; \infty$ 
C)  $- \infty ; \infty$ 
D)  5,5

Question 12

Determine the vertical asymptote(s) of the graph of the function.
-$$h ( x ) = \frac { x + 4 } { 2 x ^ { 2 } + 11 x + 5 }$$

Accepted Answer

A)  $x = - \frac { 1 } { 2 }$ and $x = - 5$ 
B)  $x = \frac { 1 } { 2 }$ and $x = - 5$ 
C)  $x = \frac { 1 } { 2 }$ and $x = - \frac { 5 } { 2 }$ 
D)  $x = 4$ and $x = 5$ 
A)  $x = - \frac { 1 } { 2 }$ and $x = - 5$ 
B)  $x = \frac { 1 } { 2 }$ and $x = - 5$ 
C)  $x = \frac { 1 } { 2 }$ and $x = - \frac { 5 } { 2 }$ 
D)  $x = 4$ and $x = 5$

Question 13

Graph the function.
-$$h ( x ) = - \frac { 1 } { 3 } ( x - 3 ) ^ { 2 } + 6$$

Accepted Answer

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

Question 14

Identify the asymptotes.
-$$r ( x ) = \frac { 4 x + 5 } { x ^ { 3 } - 5 x ^ { 2 } - 9 x + 45 }$$

Accepted Answer

A)  horizontal asymptote: $y = 0$ 
B)  Vertical asymptotes: $x = - 3 , x = 3$, and $x = 5$; horizontal asymptote: $y = - \frac { 5 } { 4 }$ 
C)  Vertical asymptotes: $x = - 3 , x = 3$, and $x = 5$; horizontal asymptote: $y = 0$ 
D)  Vertical asymptotes: $x = - 3 , x = 3$, and $x = - 5$; horizontal asymptote: $y = 0$ 
A)  horizontal asymptote: $y = 0$ 
B)  Vertical asymptotes: $x = - 3 , x = 3$, and $x = 5$; horizontal asymptote: $y = - \frac { 5 } { 4 }$ 
C)  Vertical asymptotes: $x = - 3 , x = 3$, and $x = 5$; horizontal asymptote: $y = 0$ 
D)  Vertical asymptotes: $x = - 3 , x = 3$, and $x = - 5$; horizontal asymptote: $y = 0$

Question 15

Choose the one alternative that best completes the statement or answers the question.
Determine the end behavior of the graph of the function.
-$$f ( x ) = 8 x ^ { 3 } ( 4 - x ) ( 7 x - 6 ) ^ { 4 }$$

Accepted Answer

A)  Down left and down right 
B)  Up left and down right 
C)  Down left and up right 
D)  Up left and up right 
A)  Down left and down right 
B)  Up left and down right 
C)  Down left and up right 
D)  Up left and up right

Question 16

Write a polynomial f (x) that meets the given conditions.
-Polynomial of lowest degree with real coefficients and zeros $4 i$ and $2 - i$.

Accepted Answer

A)  $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 12 x ^ { 2 } + 64 x - 64$ 
B)  $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 19 x ^ { 2 } - 64 x + 48$ 
C)  $f ( x ) = x ^ { 4 } + 4 x ^ { 3 } - 12 x ^ { 2 } - 64 x + 64$ 
D)  $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 21 x ^ { 2 } - 64 x + 80$ 
A)  $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 12 x ^ { 2 } + 64 x - 64$ 
B)  $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 19 x ^ { 2 } - 64 x + 48$ 
C)  $f ( x ) = x ^ { 4 } + 4 x ^ { 3 } - 12 x ^ { 2 } - 64 x + 64$ 
D)  $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 21 x ^ { 2 } - 64 x + 80$

Question 17

Solve the inequality. Write the solution set in interval notation.
-$$w ^ { 4 } - 29 w ^ { 2 } + 100 \leq 0$$

Accepted Answer

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

Question 18

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The end behavior of the graph of $f ( x ) = - 8 x ^ { 3 }$ is (up/down) to the left and (up/down) to the right.

Accepted Answer

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

Question 19

Solve the problem.
-$$p ( x ) = 3 ( x + 3 ) ^ { 3 } - 3$$
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. $y = x ^ { 3 }$
b. Shift $y = x ^ { 3 }$ to the left 3 units. Stretch vertically by a factor of 3 . Shift downward 3 units.
c. Graph iii. 
B)  a. $y = x ^ { 3 }$
b. Shift $y = x ^ { 3 }$ to the left 3 units. Stretch vertically by a factor of 3 . Shift downward 3 units.
c. Graph ii. 
C)  a. $y = x ^ { 3 }$
b. Shift $y = x ^ { 3 }$ to the left 3 units. Stretch vertically by a factor of 3 . Shift downward 3 units.
c. Graph i. 
D)  a. $y = x ^ { 3 }$
b. Shift $y = x ^ { 3 }$ to the left 3 units. Shrink vertically by a factor of $\frac { 1 } { 3 }$. Shift downward 3 units.
c. Graph iv. 
A)  a. $y = x ^ { 3 }$
b. Shift $y = x ^ { 3 }$ to the left 3 units. Stretch vertically by a factor of 3 . Shift downward 3 units.
c. Graph iii. 
B)  a. $y = x ^ { 3 }$
b. Shift $y = x ^ { 3 }$ to the left 3 units. Stretch vertically by a factor of 3 . Shift downward 3 units.
c. Graph ii. 
C)  a. $y = x ^ { 3 }$
b. Shift $y = x ^ { 3 }$ to the left 3 units. Stretch vertically by a factor of 3 . Shift downward 3 units.
c. Graph i. 
D)  a. $y = x ^ { 3 }$
b. Shift $y = x ^ { 3 }$ to the left 3 units. Shrink vertically by a factor of $\frac { 1 } { 3 }$. Shift downward 3 units.
c. Graph iv.

Question 20

Determine if the statement is true or false.
-A polynomial with real coefficients of degree 11 must have at least one real zero.

Accepted Answer

A) True 
 B)False

Solve the inequality. Write the solution set in interval notation. - $\frac { 3 x - 4 } { 3 + 2 x } < 0$

Solve the problem. -The following table represents the result of a synthetic division. -2 -9 -8 5 -8 18 -20 30 -9 10 -15 \mid22 Use $x$ as the variable. Identify the quotient.

Find the zeros of the function and state the multiplicities. - $f ( x ) = - 2 x ^ { 6 } ( x + 7 ) ^ { 2 } ( x - 5 ) ^ { 6 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given a polynomial f (x), the factor theorem indicates that if f (c) = 0, then x - c is a of f (x). Furthermore, if x - c is a factor of f (x), then f (c) = .

Determine the number of possible positive and negative real zeros for the given function. - $f ( x ) = - 8 x ^ { 7 } - 7 x ^ { 4 } - 6 x ^ { 3 } + 4 x ^ { 2 } + 6 x + 5$

Refer to the graph of the function and complete the statements. -The domain isــــــــــــ The range isــــــــــــــــ

Write the domain and range of the function in interval notation. - $f ( x ) = x ^ { 2 } + 10 x + 6$

Choose the one alternative that best completes the statement or answers the question. Use long division to divide. - $\frac { 64 x ^ { 3 } + 1 } { 4 x + 1 }$

The graph of y = f (x) is given. Solve the inequality. - $f ( x ) \leq 0$ $The graph of y = f (x) is given. Solve the inequality. - f ( x ) \leq 0$

Solve the inequality. Write the solution set in interval notation. - $\frac { 40 - 8 x } { x ^ { 2 } } \leq 0$

Determine the vertical asymptote(s) of the graph of the function. - $h ( x ) = \frac { x + 4 } { 2 x ^ { 2 } + 11 x + 5 }$

Graph the function. - $h ( x ) = - \frac { 1 } { 3 } ( x - 3 ) ^ { 2 } + 6$

Identify the asymptotes. - $r ( x ) = \frac { 4 x + 5 } { x ^ { 3 } - 5 x ^ { 2 } - 9 x + 45 }$

Choose the one alternative that best completes the statement or answers the question. Determine the end behavior of the graph of the function. - $f ( x ) = 8 x ^ { 3 } ( 4 - x ) ( 7 x - 6 ) ^ { 4 }$

Write a polynomial f (x) that meets the given conditions. -Polynomial of lowest degree with real coefficients and zeros $4 i$ and $2 - i$ .

Solve the inequality. Write the solution set in interval notation. - $w ^ { 4 } - 29 w ^ { 2 } + 100 \leq 0$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The end behavior of the graph of $f ( x ) = - 8 x ^ { 3 }$ is (up/down) to the left and (up/down) to the right.

Determine if the statement is true or false. -A polynomial with real coefficients of degree 11 must have at least one real zero.

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. - 3x−43+2x<0\frac { 3 x - 4 } { 3 + 2 x } < 03+2x3x−4​<0

Solve the problem. -The following table represents the result of a synthetic division. -2 -9 -8 5 -8 18 -20 30 -9 10 -15 \mid22 Use xxx as the variable. Identify the quotient.

Find the zeros of the function and state the multiplicities. - f(x)=−2x6(x+7)2(x−5)6f ( x ) = - 2 x ^ { 6 } ( x + 7 ) ^ { 2 } ( x - 5 ) ^ { 6 }f(x)=−2x6(x+7)2(x−5)6

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Given a polynomial f (x), the factor theorem indicates that if f (c) = 0, then x - c is a of f (x). Furthermore, if x - c is a factor of f (x), then f (c) = .

Determine the number of possible positive and negative real zeros for the given function. - f(x)=−8x7−7x4−6x3+4x2+6x+5f ( x ) = - 8 x ^ { 7 } - 7 x ^ { 4 } - 6 x ^ { 3 } + 4 x ^ { 2 } + 6 x + 5f(x)=−8x7−7x4−6x3+4x2+6x+5

Refer to the graph of the function and complete the statements. -The domain isــــــــــــ The range isــــــــــــــــ

Write the domain and range of the function in interval notation. - f(x)=x2+10x+6f ( x ) = x ^ { 2 } + 10 x + 6f(x)=x2+10x+6

Choose the one alternative that best completes the statement or answers the question. Use long division to divide. - 64x3+14x+1\frac { 64 x ^ { 3 } + 1 } { 4 x + 1 }4x+164x3+1​

The graph of y = f (x) is given. Solve the inequality. - f(x)≤0f ( x ) \leq 0f(x)≤0

Solve the inequality. Write the solution set in interval notation. - 40−8xx2≤0\frac { 40 - 8 x } { x ^ { 2 } } \leq 0x240−8x​≤0

Refer to the graph of the function and complete the statements. -As x→−∞,f(x)→x \rightarrow - \infty , f ( x ) \rightarrowx→−∞,f(x)→ ــــــــــــــــــــ As x→∞,f(x)→x \rightarrow \infty , f ( x ) \rightarrowx→∞,f(x)→ ــــــــــــــ

Determine the vertical asymptote(s) of the graph of the function. - h(x)=x+42x2+11x+5h ( x ) = \frac { x + 4 } { 2 x ^ { 2 } + 11 x + 5 }h(x)=2x2+11x+5x+4​

Graph the function. - h(x)=−13(x−3)2+6h ( x ) = - \frac { 1 } { 3 } ( x - 3 ) ^ { 2 } + 6h(x)=−31​(x−3)2+6

Identify the asymptotes. - r(x)=4x+5x3−5x2−9x+45r ( x ) = \frac { 4 x + 5 } { x ^ { 3 } - 5 x ^ { 2 } - 9 x + 45 }r(x)=x3−5x2−9x+454x+5​

Choose the one alternative that best completes the statement or answers the question. Determine the end behavior of the graph of the function. - f(x)=8x3(4−x)(7x−6)4f ( x ) = 8 x ^ { 3 } ( 4 - x ) ( 7 x - 6 ) ^ { 4 }f(x)=8x3(4−x)(7x−6)4

Write a polynomial f (x) that meets the given conditions. -Polynomial of lowest degree with real coefficients and zeros 4i4 i4i and 2−i2 - i2−i .

Solve the inequality. Write the solution set in interval notation. - w4−29w2+100≤0w ^ { 4 } - 29 w ^ { 2 } + 100 \leq 0w4−29w2+100≤0

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The end behavior of the graph of f(x)=−8x3f ( x ) = - 8 x ^ { 3 }f(x)=−8x3 is (up/down) to the left and (up/down) to the right.