Question 1

Solve the inequality. Write the solution set in interval notation.
-$$( x + 7 ) ( x + 11 ) \leq - 4$$

Accepted Answer

A)  $\{ - 9 \}$ 
B)  \{ \} 
C)  $( - \infty , \infty )$ 
D)  $[ - 11 , - 7 ]$ 
A)  $\{ - 9 \}$ 
B)  \{ \} 
C)  $( - \infty , \infty )$ 
D)  $[ - 11 , - 7 ]$

Question 2

Find the zeros of the function and state the multiplicities.
-$$f ( x ) = 4 x ^ { 4 } - 101 x ^ { 2 } + 25$$

Accepted Answer

A)  $\frac { 1 } { 4 } , 25$; each of multiplicity 1 
B)  $- 5 , - \frac { 1 } { 2 } , \frac { 1 } { 2 } , 5$; each of multiplicity 1 
C)  $\frac { 1 } { 2 } , 5$; each of multiplicity 1 
D)  $- \frac { 1 } { 4 } , - 25$; each of multiplicity 1 
A)  $\frac { 1 } { 4 } , 25$; each of multiplicity 1 
B)  $- 5 , - \frac { 1 } { 2 } , \frac { 1 } { 2 } , 5$; each of multiplicity 1 
C)  $\frac { 1 } { 2 } , 5$; each of multiplicity 1 
D)  $- \frac { 1 } { 4 } , - 25$; each of multiplicity 1

Question 3

Use synthetic division to divide the polynomials.
-$$\left( 7 w ^ { 3 } + 2 w ^ { 2 } - 3 w - 14 \right) \div ( w - 1 )$$

Accepted Answer

A)  $7 w ^ { 2 } + 9 w + 6$ 
B)  $7 w ^ { 2 } + 9 w + 6 - \frac { 8 } { w - 1 }$ 
C)  $7 w ^ { 2 } + 7 w + 2 - \frac { 16 } { w + 1 }$ 
D)  $7 w ^ { 2 } + 9 w - 6$ 
A)  $7 w ^ { 2 } + 9 w + 6$ 
B)  $7 w ^ { 2 } + 9 w + 6 - \frac { 8 } { w - 1 }$ 
C)  $7 w ^ { 2 } + 7 w + 2 - \frac { 16 } { w + 1 }$ 
D)  $7 w ^ { 2 } + 9 w - 6$

Question 4

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

As $ x \rightarrow \infty, f(x) \rightarrow $ـــــــــــــــــــــــــــــ

Accepted Answer

A)  $\infty ; - \infty$ 
B)  $3 ; 3$ 
C)  $- \infty ; \infty$ 
D)  $- 5 ; - 5$ 
A)  $\infty ; - \infty$ 
B)  $3 ; 3$ 
C)  $- \infty ; \infty$ 
D)  $- 5 ; - 5$

Question 5

Solve the inequality. Write the solution set in interval notation.
-$$- x ^ { 2 } - 10 x - 24 \leq 0$$

Accepted Answer

A)  $( - \infty , 4 ] \cup [ 6 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $( - \infty , - 4 ] \cup [ 6 , \infty )$ 
D)  $( - \infty , - 6 ] \cup [ - 4 , \infty )$ 
A)  $( - \infty , 4 ] \cup [ 6 , \infty )$ 
B)  $( - \infty , \infty )$ 
C)  $( - \infty , - 4 ] \cup [ 6 , \infty )$ 
D)  $( - \infty , - 6 ] \cup [ - 4 , \infty )$

Question 6

Find the vertex of the parabola.
-$$h ( x ) = - 2 x ^ { 2 } + 12 x - 19$$

Accepted Answer

A)  $( - 3 , - 1 )$ 
B)  $( - 1 , - 3 )$ 
C)  $( 0 , - 19 )$ 
D)  $( 3 , - 1 )$ 
A)  $( - 3 , - 1 )$ 
B)  $( - 1 , - 3 )$ 
C)  $( 0 , - 19 )$ 
D)  $( 3 , - 1 )$

Question 7

Solve the problem.
-The yield on a bond varies inversely as the price. The yield on a particular bond is $3 \%$ when the price is $\$ 150$. What price is necessary for a yield of $4.5 \%$ ? Round to the nearest cent, if necessary.

Accepted Answer

A)  $\$ 9.00$ 
B)  $\$ 111.11$ 
C)  $\$ 100.00$ 
D)  \$225.00 
A)  $\$ 9.00$ 
B)  $\$ 111.11$ 
C)  $\$ 100.00$ 
D)  \$225.00

Question 8

Choose the one alternative that best completes the statement or answers the question.
Use long division to divide.
-$$\left( 4 x ^ { 3 } - 17 x ^ { 2 } - 1 x + 29 \right) \div ( x - 4 )$$

Accepted Answer

A)  $4 x ^ { 2 } - 33 x - 364$ 
B)  $4 x ^ { 2 } - 1 x + 4$ 
C)  $4 x ^ { 2 } - 1 x - 5 + \frac { 9 } { x - 4 }$ 
D)  $4 x ^ { 2 } - 33 x + 131 - \frac { 495 } { x - 4 }$ 
A)  $4 x ^ { 2 } - 33 x - 364$ 
B)  $4 x ^ { 2 } - 1 x + 4$ 
C)  $4 x ^ { 2 } - 1 x - 5 + \frac { 9 } { x - 4 }$ 
D)  $4 x ^ { 2 } - 33 x + 131 - \frac { 495 } { x - 4 }$

Question 9

Write the domain of the function in interval notation.
-$$k ( x ) = \frac { 1 } { \sqrt { 2 x ^ { 2 } + 3 x - 54 } }$$

Accepted Answer

A)  $( - \infty , - 6 ) \cup \left( \frac { 9 } { 2 } , \infty \right)$ 
B)  $\left( - 6 , \frac { 9 } { 2 } \right)$ 
C)  \{ \} 
D)  $( - \infty , \infty )$ 
A)  $( - \infty , - 6 ) \cup \left( \frac { 9 } { 2 } , \infty \right)$ 
B)  $\left( - 6 , \frac { 9 } { 2 } \right)$ 
C)  \{ \} 
D)  $( - \infty , \infty )$

Question 10

Write a polynomial f (x) that meets the given conditions. Answers may vary.
-Degree 4 polynomial with zeros 4 and $- \frac { 6 } { 5 }$ (each with multiplicity 1 ) and 0 (with multiplicity 2 ).

Accepted Answer

A)  $f ( x ) = 6 x ^ { 4 } - 29 x ^ { 3 } - 20 x ^ { 2 }$ 
B)  $f ( x ) = 6 x ^ { 4 } - 19 x ^ { 3 } - 20 x ^ { 2 }$ 
C)  $f ( x ) = 5 x ^ { 4 } - 14 x ^ { 3 } - 24 x ^ { 2 }$ 
D)  $f ( x ) = 5 x ^ { 4 } - 26 x ^ { 3 } + 24 x ^ { 2 }$ 
A)  $f ( x ) = 6 x ^ { 4 } - 29 x ^ { 3 } - 20 x ^ { 2 }$ 
B)  $f ( x ) = 6 x ^ { 4 } - 19 x ^ { 3 } - 20 x ^ { 2 }$ 
C)  $f ( x ) = 5 x ^ { 4 } - 14 x ^ { 3 } - 24 x ^ { 2 }$ 
D)  $f ( x ) = 5 x ^ { 4 } - 26 x ^ { 3 } + 24 x ^ { 2 }$

Question 11

Write a polynomial f (x) that meets the given conditions.
-Polynomial of lowest degree with zeros of $\frac { 3 } { 4 }$ (multiplicity 2 ) and $\frac { 1 } { 3 }$ (multiplicity 1 ) and with $f ( 0 ) = - 18$

Accepted Answer

A)  $f ( x ) = 96 x ^ { 3 } - 176 x ^ { 2 } + 102 x - 18$ 
B)  $f ( x ) = 48 x ^ { 3 } - 88 x ^ { 2 } + 51 x - 18$ 
C)  $f ( x ) = 96 x ^ { 3 } - 176 x ^ { 2 } - 6 x - 18$ 
D)  $f ( x ) = 48 x ^ { 3 } - 88 x ^ { 2 } + 3 x - 18$ 
A)  $f ( x ) = 96 x ^ { 3 } - 176 x ^ { 2 } + 102 x - 18$ 
B)  $f ( x ) = 48 x ^ { 3 } - 88 x ^ { 2 } + 51 x - 18$ 
C)  $f ( x ) = 96 x ^ { 3 } - 176 x ^ { 2 } - 6 x - 18$ 
D)  $f ( x ) = 48 x ^ { 3 } - 88 x ^ { 2 } + 3 x - 18$

Question 12

Find the constant of variation k.
-y varies directly as x. When x is 16, y is 20.

Accepted Answer

A)  $k = 320$ 
B)  $k = \frac { 16 } { 5 }$ 
C)  $k = \frac { 5 } { 4 }$ 
D)  $k = 80$ 
A)  $k = 320$ 
B)  $k = \frac { 16 } { 5 }$ 
C)  $k = \frac { 5 } { 4 }$ 
D)  $k = 80$

Question 13

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

Accepted Answer

A)  $x = - 4$ and $x = \frac { 1 } { 4 }$ 
B)  $x = 4$ and $x = - 4$ 
C)  None 
D)  $x = 4$ and $x = 0$ 
A)  $x = - 4$ and $x = \frac { 1 } { 4 }$ 
B)  $x = 4$ and $x = - 4$ 
C)  None 
D)  $x = 4$ and $x = 0$

Question 14

Sketch the function and determine the axis of symmetry.
-$$f ( x ) = 2 x ^ { 2 } - 4 x + 6$$

Accepted Answer

A)  Axis of symmetry: $x = - 1$
  
B)  Axis of symmetry: $x = 4$
  
C)  Axis of symmetry: $x = 1$
  
D)  Axis of symmetry: $x = - 4$
  
A)  Axis of symmetry: $x = - 1$
  
B)  Axis of symmetry: $x = 4$
  
C)  Axis of symmetry: $x = 1$
  
D)  Axis of symmetry: $x = - 4$

Question 15

Solve the problem.
-Tetanus bacillus bacteria are cultured to produce tetanus toxin used in an inactive form for the
tetanus vaccine. The amount of toxin produced per batch increases with time and then decreases as
the culture becomes unstable. The variable t is the time in hours after the culture has started, and y
t is the yield of toxin in grams. $\begin{array}{l|llllllllllll}
t & 8 & 16 & 24 & 32 & 40 & 48 & 56 & 64 & 72 & 80 & 88 & 96 \
\hline y(t) & 0.55 & 1.13 & 1.62 & 1.80 & 1.88 & 1.98 & 1.92 & 1.78 & 1.51 & 1.33 & 0.69 & 0.13
\end{array}$

a. Use regression to find a quadratic function to model the data.
b. At what time is the yield the greatest? Round to the nearest hour.
A) a. $y = - 0.000831 t ^ { 2 } + 0.081 t + 0.028$
b. $51 \mathrm { hr }$

B) a. $y = - 0.0008148 t ^ { 2 } + 0.08155 t + 0.646$
b. $49 \mathrm { hr }$

C) a. $y = - 0.0008148 t ^ { 2 } + 0.08155 t + 0.646$
b. $50 \mathrm { hr }$

D) a. $y = - 0.000831 t ^ { 2 } + 0.081 t + 0.028$
b. $49 \mathrm { hr }$

Accepted Answer

D Determine the number of @#LAT-DLM&-int

Question 16

Write the word or phrase that best completes each statement or answers the question.
Provide the missing information.
-The domain of a rational function defined by $f ( x ) = \frac { p ( x ) } { q ( x ) }$ is all real numbers excluding the zeros of
.

Accepted Answer

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

Question 17

Write the domain of the function in interval notation.
-$$p ( x ) = \sqrt { x ^ { 2 } - 14 }$$

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $( - \infty , - \sqrt { 14 } ] \cup [ \sqrt { 14 } , \infty )$ 
C)  $[ - \sqrt { 14 } , \sqrt { 14 } ]$ 
D)  $[ \sqrt { 14 } , \infty )$ 
A)  $( - \infty , \infty )$ 
B)  $( - \infty , - \sqrt { 14 } ] \cup [ \sqrt { 14 } , \infty )$ 
C)  $[ - \sqrt { 14 } , \sqrt { 14 } ]$ 
D)  $[ \sqrt { 14 } , \infty )$

Question 18

Write the function in vertex form and determine the range.
-$$f ( x ) = - 3 x ^ { 2 } + 18 x - 33$$

Accepted Answer

A)  $f ( x ) = - 3 ( x - 3 ) ^ { 2 } - 6$
Range: $( - \infty , - 6 ]$ 
B)  $f ( x ) = - 3 ( x + 3 ) ^ { 2 } - 6$
Range: $( - \infty , - 6 ]$ 
C)  $f ( x ) = - 3 ( x + 3 ) ^ { 2 } - 6$
Range: $[ 3 , \infty )$ 
D)  $f ( x ) = - 3 ( x - 3 ) ^ { 2 } - 6$
Range: $[ 3 , \infty )$ 
A)  $f ( x ) = - 3 ( x - 3 ) ^ { 2 } - 6$
Range: $( - \infty , - 6 ]$ 
B)  $f ( x ) = - 3 ( x + 3 ) ^ { 2 } - 6$
Range: $( - \infty , - 6 ]$ 
C)  $f ( x ) = - 3 ( x + 3 ) ^ { 2 } - 6$
Range: $[ 3 , \infty )$ 
D)  $f ( x ) = - 3 ( x - 3 ) ^ { 2 } - 6$
Range: $[ 3 , \infty )$

Question 19

Find all the rational zeros.
-$$f ( x ) = x ^ { 4 } - 6 x ^ { 3 } - 5 x ^ { 2 } - 12 x - 14$$

Accepted Answer

A)  $\pm 1 , \pm 7 , \pm 2$ 
B)  $- 1,7 , - 2$ 
C)  $\pm 1 , \pm 7$ 
D)  $- 1,7$ 
A)  $\pm 1 , \pm 7 , \pm 2$ 
B)  $- 1,7 , - 2$ 
C)  $\pm 1 , \pm 7$ 
D)  $- 1,7$

Question 20

Find the vertex of the parabola by applying the vertex formula.
-$$h ( a ) = 6 a ^ { 2 } + 16$$

Accepted Answer

A)  $\left( \frac { 1 } { 12 } , \frac { 385 } { 24 } \right)$ 
B)  $\left( \frac { 1 } { 12 } , - \frac { 385 } { 24 } \right)$ 
C)  $( 0 , - 16 )$ 
D)  $( 0,16 )$ 
A)  $\left( \frac { 1 } { 12 } , \frac { 385 } { 24 } \right)$ 
B)  $\left( \frac { 1 } { 12 } , - \frac { 385 } { 24 } \right)$ 
C)  $( 0 , - 16 )$ 
D)  $( 0,16 )$

Solve the inequality. Write the solution set in interval notation. - $( x + 7 ) ( x + 11 ) \leq - 4$

Find the zeros of the function and state the multiplicities. - $f ( x ) = 4 x ^ { 4 } - 101 x ^ { 2 } + 25$

Use synthetic division to divide the polynomials. - $\left( 7 w ^ { 3 } + 2 w ^ { 2 } - 3 w - 14 \right) \div ( w - 1 )$

Solve the inequality. Write the solution set in interval notation. - $- x ^ { 2 } - 10 x - 24 \leq 0$

Find the vertex of the parabola. - $h ( x ) = - 2 x ^ { 2 } + 12 x - 19$

Solve the problem. -The yield on a bond varies inversely as the price. The yield on a particular bond is $3 \%$ when the price is $\$ 150$ . What price is necessary for a yield of $4.5 \%$ ? Round to the nearest cent, if necessary.

Choose the one alternative that best completes the statement or answers the question. Use long division to divide. - $\left( 4 x ^ { 3 } - 17 x ^ { 2 } - 1 x + 29 \right) \div ( x - 4 )$

Write the domain of the function in interval notation. - $k ( x ) = \frac { 1 } { \sqrt { 2 x ^ { 2 } + 3 x - 54 } }$

Write a polynomial f (x) that meets the given conditions. Answers may vary. -Degree 4 polynomial with zeros 4 and $- \frac { 6 } { 5 }$ (each with multiplicity 1 ) and 0 (with multiplicity 2 ).

Write a polynomial f (x) that meets the given conditions. -Polynomial of lowest degree with zeros of $\frac { 3 } { 4 }$ (multiplicity 2 ) and $\frac { 1 } { 3 }$ (multiplicity 1 ) and with $f ( 0 ) = - 18$

Find the constant of variation k. -y varies directly as x. When x is 16, y is 20.

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

Sketch the function and determine the axis of symmetry. - $f ( x ) = 2 x ^ { 2 } - 4 x + 6$

Write the word or phrase that best completes each statement or answers the question. Provide the missing information. -The domain of a rational function defined by $f ( x ) = \frac { p ( x ) } { q ( x ) }$ is all real numbers excluding the zeros of .

Write the domain of the function in interval notation. - $p ( x ) = \sqrt { x ^ { 2 } - 14 }$

Write the function in vertex form and determine the range. - $f ( x ) = - 3 x ^ { 2 } + 18 x - 33$

Find all the rational zeros. - $f ( x ) = x ^ { 4 } - 6 x ^ { 3 } - 5 x ^ { 2 } - 12 x - 14$

Find the vertex of the parabola by applying the vertex formula. - $h ( a ) = 6 a ^ { 2 } + 16$

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

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Exam 3: Polynomial and Rational Functions

Solve the inequality. Write the solution set in interval notation. - (x+7)(x+11)≤−4( x + 7 ) ( x + 11 ) \leq - 4(x+7)(x+11)≤−4

Find the zeros of the function and state the multiplicities. - f(x)=4x4−101x2+25f ( x ) = 4 x ^ { 4 } - 101 x ^ { 2 } + 25f(x)=4x4−101x2+25

Use synthetic division to divide the polynomials. - (7w3+2w2−3w−14)÷(w−1)\left( 7 w ^ { 3 } + 2 w ^ { 2 } - 3 w - 14 \right) \div ( w - 1 )(7w3+2w2−3w−14)÷(w−1)

Solve the inequality. Write the solution set in interval notation. - −x2−10x−24≤0- x ^ { 2 } - 10 x - 24 \leq 0−x2−10x−24≤0

Find the vertex of the parabola. - h(x)=−2x2+12x−19h ( x ) = - 2 x ^ { 2 } + 12 x - 19h(x)=−2x2+12x−19

Solve the problem. -The yield on a bond varies inversely as the price. The yield on a particular bond is 3%3 \%3% when the price is $150\$ 150$150 . What price is necessary for a yield of 4.5%4.5 \%4.5% ? Round to the nearest cent, if necessary.

Choose the one alternative that best completes the statement or answers the question. Use long division to divide. - (4x3−17x2−1x+29)÷(x−4)\left( 4 x ^ { 3 } - 17 x ^ { 2 } - 1 x + 29 \right) \div ( x - 4 )(4x3−17x2−1x+29)÷(x−4)

Write the domain of the function in interval notation. - k(x)=12x2+3x−54k ( x ) = \frac { 1 } { \sqrt { 2 x ^ { 2 } + 3 x - 54 } }k(x)=2x2+3x−54​1​

Write a polynomial f (x) that meets the given conditions. Answers may vary. -Degree 4 polynomial with zeros 4 and −65- \frac { 6 } { 5 }−56​ (each with multiplicity 1 ) and 0 (with multiplicity 2 ).

Write a polynomial f (x) that meets the given conditions. -Polynomial of lowest degree with zeros of 34\frac { 3 } { 4 }43​ (multiplicity 2 ) and 13\frac { 1 } { 3 }31​ (multiplicity 1 ) and with f(0)=−18f ( 0 ) = - 18f(0)=−18