Question 1

Solve the inequality. Write the solution set in interval notation.
-$$d ^ { 2 } > 9 d$$

Accepted Answer

A)  $( 0,9 )$ 
B)  $( - \infty , 0 ) \cup ( 9 , \infty )$ 
C)  $( 9 , \infty )$ 
D)  $( - \infty , 9 ]$ 
A)  $( 0,9 )$ 
B)  $( - \infty , 0 ) \cup ( 9 , \infty )$ 
C)  $( 9 , \infty )$ 
D)  $( - \infty , 9 ]$

Question 2

Use the remainder theorem to determine if the given binomial is a factor of f (x).
-$$f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 28 x - 84 ; \quad x - 5 \sqrt { 7 }$$

Accepted Answer

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

Question 3

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-A real number b is called a(n) bound of the real zeros of a polynomial f (x) if all real
zeros of f (x) are less than or equal to b.

Accepted Answer

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

Question 4

Write the function in vertex form and determine the x-intercept(s)
-$$p ( x ) = x ^ { 2 } + 9 x + 11$$

Accepted Answer

A)  $p ( x ) = \left( x + \frac { 9 } { 2 } \right) ^ { 2 } - \frac { 37 } { 4 } ; \left( \frac { - 9 + \sqrt { 37 } } { 2 } , 0 \right)$ and $\left( \frac { - 9 - \sqrt { 37 } } { 2 } , 0 \right)$ 
B)  $p ( x ) = \left( x + \frac { 9 } { 2 } \right) ^ { 2 } + \frac { 37 } { 4 } ; \left( \frac { - 9 + \sqrt { 37 } } { 2 } , 0 \right)$ and $\left( \frac { - 9 - \sqrt { 37 } } { 2 } , 0 \right)$ 
C)  $p ( x ) = \left( x - \frac { 9 } { 2 } \right) ^ { 2 } - \frac { 37 } { 4 } ; ( 0,0 )$ 
D)  $p ( x ) = \left( x + \frac { 9 } { 2 } \right) ^ { 2 } - \frac { 37 } { 4 } ; ( 0,0 )$ 
A)  $p ( x ) = \left( x + \frac { 9 } { 2 } \right) ^ { 2 } - \frac { 37 } { 4 } ; \left( \frac { - 9 + \sqrt { 37 } } { 2 } , 0 \right)$ and $\left( \frac { - 9 - \sqrt { 37 } } { 2 } , 0 \right)$ 
B)  $p ( x ) = \left( x + \frac { 9 } { 2 } \right) ^ { 2 } + \frac { 37 } { 4 } ; \left( \frac { - 9 + \sqrt { 37 } } { 2 } , 0 \right)$ and $\left( \frac { - 9 - \sqrt { 37 } } { 2 } , 0 \right)$ 
C)  $p ( x ) = \left( x - \frac { 9 } { 2 } \right) ^ { 2 } - \frac { 37 } { 4 } ; ( 0,0 )$ 
D)  $p ( x ) = \left( x + \frac { 9 } { 2 } \right) ^ { 2 } - \frac { 37 } { 4 } ; ( 0,0 )$

Question 5

Solve the problem.
-The population $P ( t )$ of a bacteria culture is given by $P ( t ) = - 1,500 t ^ { 2 } + 48,000 t + 18,000$, where $t$ is the time in hours after the culture is started. Determine the time(s) at which the population will be greater than 388,500 organisms.

Accepted Answer

A)  The population will be greater than 388,500 organisms from $19 \mathrm { hr }$ after the culture is started. 
B)  The population will be greater than 388,500 organisms from $25 \mathrm { hr }$ after the culture is started. 
C)  The population will be greater than 388,500 organisms between $13 \mathrm { hr }$ and $25 \mathrm { hr }$ after the culture is started. 
D)  The population will be greater than 388,500 organisms between $13 \mathrm { hr }$ and $19 \mathrm { hr }$ after the culture is started. 
A)  The population will be greater than 388,500 organisms from $19 \mathrm { hr }$ after the culture is started. 
B)  The population will be greater than 388,500 organisms from $25 \mathrm { hr }$ after the culture is started. 
C)  The population will be greater than 388,500 organisms between $13 \mathrm { hr }$ and $25 \mathrm { hr }$ after the culture is started. 
D)  The population will be greater than 388,500 organisms between $13 \mathrm { hr }$ and $19 \mathrm { hr }$ after the culture is started.

Question 6

Solve the inequality. Write the solution set in interval notation.
-$$- 2 > ( 5 x + 8 ) ^ { 2 }$$

Accepted Answer

A)  $\left( - \frac { 8 } { 5 } , \infty \right)$ 
B)  $\left[ - \frac { 8 } { 5 } , \infty \right)$ 
C)  \{ \} 
D)  $( - \infty , \infty )$ 
A)  $\left( - \frac { 8 } { 5 } , \infty \right)$ 
B)  $\left[ - \frac { 8 } { 5 } , \infty \right)$ 
C)  \{ \} 
D)  $( - \infty , \infty )$

Question 7

Determine if the graph can represent a polynomial function. If so, assume the end behavior and all turning points are represented on the graph.
-  
a. Determine the minimum degree of the polynomial based on the number of turning points. 
b. Determine whether the leading coefficient is positive or negative based on the end behavior and Whether the degree of the polynomial is odd or even.
c. Approximate the real zeros of the function, and determine if their multiplicity is odd or even.

Accepted Answer

A)  a. Minimum degree 3
b. Leading coefficient positive degree odd
c. $- 2,1$, and 2 (each with odd multiplicity) 
B)  a. Minimum degree 3
b. Leading coefficient negative degree odd
c. $- 2$ (odd multiplicity), 1 (even multiplicity), 2 (even multiplicity) 
C)  a. Minimum degree 2
b. Leading coefficient negative degree even
c. $- 2$ (odd multiplicity), 1 (even multiplicity), 2 (even multiplicity) 
D)  Not a polynomial function. 
A)  a. Minimum degree 3
b. Leading coefficient positive degree odd
c. $- 2,1$, and 2 (each with odd multiplicity) 
B)  a. Minimum degree 3
b. Leading coefficient negative degree odd
c. $- 2$ (odd multiplicity), 1 (even multiplicity), 2 (even multiplicity) 
C)  a. Minimum degree 2
b. Leading coefficient negative degree even
c. $- 2$ (odd multiplicity), 1 (even multiplicity), 2 (even multiplicity) 
D)  Not a polynomial function.

Question 8

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The volume of a right circular cone varies as the square of the radius of the cylinder
and as the height of the cylinder.

Accepted Answer

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

Question 9

Determine the vertical asymptote(s) of the graph of the function.
-$$f ( a ) = \frac { a ^ { 2 } + 4 } { a ^ { 2 } + 3 a - 5 }$$

Accepted Answer

A)  $a = \frac { - 3 + \sqrt { 29 } } { 2 }$ and $a = \frac { - 3 - \sqrt { 29 } } { 2 }$ 
B)  $a = 2$ and $a = - 2$ 
C)  $a = - \frac { 5 } { 3 }$ 
D)  None 
A)  $a = \frac { - 3 + \sqrt { 29 } } { 2 }$ and $a = \frac { - 3 - \sqrt { 29 } } { 2 }$ 
B)  $a = 2$ and $a = - 2$ 
C)  $a = - \frac { 5 } { 3 }$ 
D)  None

Question 10

Find the zeros of the function and state the multiplicities.
-$m ( x ) = x ^ { 5 } - 3 x ^ { 3 }$

Accepted Answer

A)  $- \sqrt { 3 } , 0 , \sqrt { 3 }$; each of multiplicity 3 
B)  $- \sqrt { 3 } , \sqrt { 3 }$ each of multiplicity 1 ; 0 of multiplicity 3 
C)  $- \sqrt { 3 } , \sqrt { 3 }$ each of multiplicity $3 ; 0$ of multiplicity 1 
D)  $- \sqrt { 3 } , 0 , \sqrt { 3 }$; each of multiplicity 1 
A)  $- \sqrt { 3 } , 0 , \sqrt { 3 }$; each of multiplicity 3 
B)  $- \sqrt { 3 } , \sqrt { 3 }$ each of multiplicity 1 ; 0 of multiplicity 3 
C)  $- \sqrt { 3 } , \sqrt { 3 }$ each of multiplicity $3 ; 0$ of multiplicity 1 
D)  $- \sqrt { 3 } , 0 , \sqrt { 3 }$; each of multiplicity 1

Question 11

Determine the x- and y-intercepts for the given function.
-$$f ( x ) = 2 x ^ { 2 } + 8 x - 10$$

Accepted Answer

A)  $x$-intercept: $( - 2,0 )$
$y$-intercept: $( 0 , - 18 )$ 
B)  $x$-intercept: none
$y$-intercept: $( 0 , - 10 )$ 
C)  $x$-intercept: $( - 2,0 )$
$y$-intercept: $( 0,18 )$ 
D)  $x$-intercepts: $( - 5,0 )$ and $( 1,0 )$
$y$-intercept: $( 0 , - 10 )$ 
A)  $x$-intercept: $( - 2,0 )$
$y$-intercept: $( 0 , - 18 )$ 
B)  $x$-intercept: none
$y$-intercept: $( 0 , - 10 )$ 
C)  $x$-intercept: $( - 2,0 )$
$y$-intercept: $( 0,18 )$ 
D)  $x$-intercepts: $( - 5,0 )$ and $( 1,0 )$
$y$-intercept: $( 0 , - 10 )$

Question 12

Solve the inequality. Write the solution set in interval notation.
-$$\frac { 9 - x } { x + 11 } \geq 0$$

Accepted Answer

A)  $( - 11,9 ]$ 
B)  $( - \infty , - 11 ) \cup ( 9 , \infty )$ 
C)  $[ - 11,9 )$ 
D)  $( - \infty , - 11 ] \cup [ 9 , \infty )$ 
A)  $( - 11,9 ]$ 
B)  $( - \infty , - 11 ) \cup ( 9 , \infty )$ 
C)  $[ - 11,9 )$ 
D)  $( - \infty , - 11 ] \cup [ 9 , \infty )$

Question 13

Choose the one alternative that best completes the statement or answers the question.
Use long division to divide.
-$\left( - 150 x ^ { 2 } + 15 x ^ { 4 } + 135 \right) \div ( 3 x + 9 )$

Accepted Answer

A)  $5 x ^ { 3 } - 15 x ^ { 2 } - 5 x + 15$ 
B)  $5 x ^ { 3 } - 65 x + \frac { 240 } { x + 3 }$ 
C)  $5 x ^ { 3 } + 15 x ^ { 2 } - 5 x - 15$ 
D)  $155 x ^ { 3 } - 50 x - \frac { 420 } { x + 3 }$ 
A)  $5 x ^ { 3 } - 15 x ^ { 2 } - 5 x + 15$ 
B)  $5 x ^ { 3 } - 65 x + \frac { 240 } { x + 3 }$ 
C)  $5 x ^ { 3 } + 15 x ^ { 2 } - 5 x - 15$ 
D)  $155 x ^ { 3 } - 50 x - \frac { 420 } { x + 3 }$

Question 14

A table of values is given for $Y _ { 1 } = f ( x )$ ). Determine whether the intermediate value theorem guarantees
that the function has a zero on the given interval.
-$\mathrm{Y}_{1}=17 x^{4}-39 x^{3}+186 x^{2}+298 x+398 \quad[-2,-1]$
$\begin{array}{r|r}
\mathrm{X} & \mathrm{Y}_{1} \
\hline-4 & 9,030 \
-3 & 3,608 \
-2 & 1,130 \
-1 & 342 \
0 & 398 \
1 & 860 \
2 & 1,698 \
3 & 3,290 \
\hline \mathrm{X}=-4 &
\end{array}$

Accepted Answer

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

Question 15

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-a. Given $y = \frac { 24 } { x }$, evaluate $y$ for the given values of $x$. $x = 1 , x = 2 , x = 3 , x = 4$, and $x = 6 .$
b. How does $y$ change when $x$ is doubled?
c. How does $y$ change when $x$ is tripled?
d. Complete the statement. Given $y = \frac { 24 } { x }$, when $x$ increases, $y$ (increases/decreases) proportionally.
e. Complete the statement. Given $y = \frac { 24 } { x }$, when $x$ decreases, $y$ (increases/decreases) proportionally.

Accepted Answer

a. @#LAT-DLM&
b. @#LAT-DLM& is one-half its origin

Question 16

Solve the inequality. Write the solution set in interval notation.
-$$36 z ^ { 2 } - 9 < 0$$

Accepted Answer

A)  $\left[ - \infty , - \frac { 1 } { 2 } \right] \cup \left[ \frac { 1 } { 2 } , \infty \right)$ 
B)  $\left( - \infty , - \frac { 1 } { 2 } \right) \cup \left( \frac { 1 } { 2 } , \infty \right)$ 
C)  $\left( - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right)$ 
D)  $\left[ - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right]$ 
A)  $\left[ - \infty , - \frac { 1 } { 2 } \right] \cup \left[ \frac { 1 } { 2 } , \infty \right)$ 
B)  $\left( - \infty , - \frac { 1 } { 2 } \right) \cup \left( \frac { 1 } { 2 } , \infty \right)$ 
C)  $\left( - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right)$ 
D)  $\left[ - \frac { 1 } { 2 } , \frac { 1 } { 2 } \right]$

Question 17

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-Explain why the number 7 cannot be a rational zero of the polynomial $$f ( x ) = 2 x ^ { 3 } + 5 x ^ { 2 } - x + 6$$

Accepted Answer

7 is not the ratio o

Question 18

Solve the problem.
-The number of hours it takes to paint a house is inversely proportional to the number of people painting. If it takes 3 workers $17.7$ hours to paint a certain house, how long would it take 5 workers? Round to one tenth of an hour.

Accepted Answer

A)  $15.7$ hours 
B)  $19.7$ hours 
C)  $10.6$ hours 
D)  $53.0$ hours 
A)  $15.7$ hours 
B)  $19.7$ hours 
C)  $10.6$ hours 
D)  $53.0$ hours

Question 19

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 m is directly proportional to n.

Accepted Answer

A)  $m = \frac { k } { n }$ 
B)  $m = k n$ 
C)  $m = k + n$ 
D)  $n = \frac { k } { m }$ 
A)  $m = \frac { k } { n }$ 
B)  $m = k n$ 
C)  $m = k + n$ 
D)  $n = \frac { k } { m }$

Question 20

Choose the one alternative that best completes the statement or answers the question.
The graph of y = f (x) is given. Solve the inequality.
-$f(x)<0$

Accepted Answer

A)  $( - \infty , 3 )$ 
B)  $\{ 0 \} \cup ( 3 , \infty )$ 
C)  $( - \infty , 0 ) \cup ( 0,3 )$ 
D)  $( 3 , \infty )$ 
A)  $( - \infty , 3 )$ 
B)  $\{ 0 \} \cup ( 3 , \infty )$ 
C)  $( - \infty , 0 ) \cup ( 0,3 )$ 
D)  $( 3 , \infty )$

Solve the inequality. Write the solution set in interval notation. - $d ^ { 2 } > 9 d$

Use the remainder theorem to determine if the given binomial is a factor of f (x). - $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 28 x - 84 ; \quad x - 5 \sqrt { 7 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A real number b is called a(n) bound of the real zeros of a polynomial f (x) if all real zeros of f (x) are less than or equal to b.

Write the function in vertex form and determine the x-intercept(s) - $p ( x ) = x ^ { 2 } + 9 x + 11$

Solve the problem. -The population $P ( t )$ of a bacteria culture is given by $P ( t ) = - 1,500 t ^ { 2 } + 48,000 t + 18,000$ , where $t$ is the time in hours after the culture is started. Determine the time(s) at which the population will be greater than 388,500 organisms.

Solve the inequality. Write the solution set in interval notation. - $- 2 > ( 5 x + 8 ) ^ { 2 }$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The volume of a right circular cone varies as the square of the radius of the cylinder and as the height of the cylinder.

Determine the vertical asymptote(s) of the graph of the function. - $f ( a ) = \frac { a ^ { 2 } + 4 } { a ^ { 2 } + 3 a - 5 }$

Find the zeros of the function and state the multiplicities. - $m ( x ) = x ^ { 5 } - 3 x ^ { 3 }$

Determine the x- and y-intercepts for the given function. - $f ( x ) = 2 x ^ { 2 } + 8 x - 10$

Solve the inequality. Write the solution set in interval notation. - $\frac { 9 - x } { x + 11 } \geq 0$

Choose the one alternative that best completes the statement or answers the question. Use long division to divide. - $\left( - 150 x ^ { 2 } + 15 x ^ { 4 } + 135 \right) \div ( 3 x + 9 )$

Solve the inequality. Write the solution set in interval notation. - $36 z ^ { 2 } - 9 < 0$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -Explain why the number 7 cannot be a rational zero of the polynomial $f ( x ) = 2 x ^ { 3 } + 5 x ^ { 2 } - x + 6$

Solve the problem. -The number of hours it takes to paint a house is inversely proportional to the number of people painting. If it takes 3 workers $17.7$ hours to paint a certain house, how long would it take 5 workers? Round to one tenth of an hour.

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 m is directly proportional to n.

Choose the one alternative that best completes the statement or answers the question. The graph of y = f (x) is given. Solve the inequality. - $f(x)<0$

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. - d2>9dd ^ { 2 } > 9 dd2>9d

Use the remainder theorem to determine if the given binomial is a factor of f (x). - f(x)=x3+3x2−28x−84;x−57f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 28 x - 84 ; \quad x - 5 \sqrt { 7 }f(x)=x3+3x2−28x−84;x−57​

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -A real number b is called a(n) bound of the real zeros of a polynomial f (x) if all real zeros of f (x) are less than or equal to b.

Write the function in vertex form and determine the x-intercept(s) - p(x)=x2+9x+11p ( x ) = x ^ { 2 } + 9 x + 11p(x)=x2+9x+11

Solve the inequality. Write the solution set in interval notation. - −2>(5x+8)2- 2 > ( 5 x + 8 ) ^ { 2 }−2>(5x+8)2