Question 1

Provide an appropriate response.
-Find a quadratic function $\mathrm { f }$ having $\mathrm { x }$-intercepts 3 and $- 4$ and $y$-intercept $- 24$.

Accepted Answer

A)  $f ( x ) = x ^ { 2 } + x - 12$ 
B)  $f ( x ) = x ^ { 2 } + 5 x - 24$ 
C)  $f ( x ) = x ^ { 2 } + x - 24$ 
D)  $f ( x ) = 2 x ^ { 2 } + 2 x - 24$ 
A)  $f ( x ) = x ^ { 2 } + x - 12$ 
B)  $f ( x ) = x ^ { 2 } + 5 x - 24$ 
C)  $f ( x ) = x ^ { 2 } + x - 24$ 
D)  $f ( x ) = 2 x ^ { 2 } + 2 x - 24$

Question 2

Solve the problem.
-The weight of a body above the surface of the earth is inversely proportional to the square of its distance from the center of the earth. What is the effect on the weight when the distance is multiplied by 4 ?

Accepted Answer

A)  The weight is divided by 16 . 
B)  The weight is divided by 4 . 
C)  The weight is multiplied by $16 .$ 
D)  The weight is multiplied by 4 . 
A)  The weight is divided by 16 . 
B)  The weight is divided by 4 . 
C)  The weight is multiplied by $16 .$ 
D)  The weight is multiplied by 4 .

Question 3

Solve the problem.
-The length of a table is 11 inches more than its width. If the area of the table is 1692 square inches, what is its length?

Accepted Answer

A)  $25 \mathrm { in }$. 
B)  47 in. 
C)  $72 \mathrm { in. }$ 
D)  $36 \mathrm { in }$. 
A)  $25 \mathrm { in }$. 
B)  47 in. 
C)  $72 \mathrm { in. }$ 
D)  $36 \mathrm { in }$.

Question 4

Give the domain and range for the rational function. Use interval notation.
-$$f ( x ) = \frac { 1 } { ( x + 8 ) ^ { 2 } }$$

Accepted Answer

A)  Domain: $( - \infty , - 8 ) \cup ( - 8 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  Domain: $( - \infty , - 8 ) \cup ( - 8 , \infty )$; Range: $( - \infty , \infty )$ 
C)  Domain: $( - \infty , - 8 ) \cup ( - 8 , \infty )$; Range: $( 0 , \infty )$ 
D)  Domain: $( - \infty , 8 ) \cup ( 8 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
A)  Domain: $( - \infty , - 8 ) \cup ( - 8 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$ 
B)  Domain: $( - \infty , - 8 ) \cup ( - 8 , \infty )$; Range: $( - \infty , \infty )$ 
C)  Domain: $( - \infty , - 8 ) \cup ( - 8 , \infty )$; Range: $( 0 , \infty )$ 
D)  Domain: $( - \infty , 8 ) \cup ( 8 , \infty )$; Range: $( - \infty , 0 ) \cup ( 0 , \infty )$

Question 5

Solve the problem.
-If the average cost per unit $C ( x )$ to produce $x$ units of plywood is given by $C ( x ) = \frac { 300 } { x + 10 }$, what is the unit cost for 20 units?

Accepted Answer

A)  $\$ 10.00$ 
B)  $\$ 5.00$ 
C)  $\$ 15.00$ 
D)  $\$ 1.50$ 
A)  $\$ 10.00$ 
B)  $\$ 5.00$ 
C)  $\$ 15.00$ 
D)  $\$ 1.50$

Question 6

Provide an appropriate response.
-Explain the behavior of the graph of $\mathrm { f } ( \mathrm { x } )$ as it approaches its vertical asymptote. $f ( x ) = \frac { 4 } { ( x - 8 ) ^ { 2 } }$

Accepted Answer

A)  Approaches $\infty$ from the left and the right 
B)  Approaches $- \infty$ from the left, approaches $\infty$ from the right 
C)  Approaches $\infty$ from the left, approaches $- \infty$ from the right 
D)  Approaches $- \infty$ from the left and the right 
A)  Approaches $\infty$ from the left and the right 
B)  Approaches $- \infty$ from the left, approaches $\infty$ from the right 
C)  Approaches $\infty$ from the left, approaches $- \infty$ from the right 
D)  Approaches $- \infty$ from the left and the right

Question 7

Express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k.
-$$f ( x ) = 3 x ^ { 4 } - 9 x ^ { 3 } + 2 x ^ { 2 } - 6 x ; \quad k = 3$$

Accepted Answer

A)  $f ( x ) = ( x - 3 ) \left( 3 x ^ { 3 } + x ^ { 2 } - x + 3 \right) + 9$ 
B)  $f ( x ) = ( x + 3 ) \left( 3 x ^ { 2 } + 2 x \right)$ 
C)  $f ( x ) = ( x + 3 ) \left( 3 x ^ { 3 } + 2 x \right)$ 
D)  $f ( x ) = ( x - 3 ) \left( 3 x ^ { 3 } + 2 x \right)$ 
A)  $f ( x ) = ( x - 3 ) \left( 3 x ^ { 3 } + x ^ { 2 } - x + 3 \right) + 9$ 
B)  $f ( x ) = ( x + 3 ) \left( 3 x ^ { 2 } + 2 x \right)$ 
C)  $f ( x ) = ( x + 3 ) \left( 3 x ^ { 3 } + 2 x \right)$ 
D)  $f ( x ) = ( x - 3 ) \left( 3 x ^ { 3 } + 2 x \right)$

Question 8

Determine which of the rational functions given below has the following feature(s).
-The $y$-intercept is 4

Accepted Answer

A)  $f ( x ) = \frac { 4 x - 1 } { x + 4 }$ 
B)  $f ( x ) = \frac { x + 8 } { x - 2 }$ 
C)  $f ( x ) = \frac { x + 4 } { x - 2 }$ 
D)  $f ( x ) = \frac { x - 8 } { x - 2 }$ 
A)  $f ( x ) = \frac { 4 x - 1 } { x + 4 }$ 
B)  $f ( x ) = \frac { x + 8 } { x - 2 }$ 
C)  $f ( x ) = \frac { x + 4 } { x - 2 }$ 
D)  $f ( x ) = \frac { x - 8 } { x - 2 }$

Question 9

Use the factor theorem to decide whether or not the second polynomial is a factor of the first.
-$$5 x ^ { 3 } + 8 x ^ { 2 } - 3 x + 2 ; x + 2$$

Accepted Answer

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

Question 10

Solve the problem.
-If an object is propelled upward from a height of 160 feet at an initial velocity of 144 feet per second, then its height after $t$ seconds is given by the equation $h ( t ) = - 16 t ^ { 2 } + 144 t + 160$. After how many seconds does the object hit the ground?

Accepted Answer

A)  $11 \mathrm { sec }$ 
B)  $5.0 \mathrm { sec }$ 
C)  $9.0 \mathrm { sec }$ 
D)  $10 \mathrm { sec }$ 
A)  $11 \mathrm { sec }$ 
B)  $5.0 \mathrm { sec }$ 
C)  $9.0 \mathrm { sec }$ 
D)  $10 \mathrm { sec }$

Question 11

Give the equation of any oblique asymptotes.
-$$f ( x ) = \frac { x ^ { 2 } + 4 x + 3 } { x + 7 }$$

Accepted Answer

A)  none 
B)  $y = x - 11$ 
C)  $x = y - 3$ 
D)  $\mathrm { y } = \mathrm { x } - 3$ 
A)  none 
B)  $y = x - 11$ 
C)  $x = y - 3$ 
D)  $\mathrm { y } = \mathrm { x } - 3$

Question 12

Solve the problem.
-A rock is propelled upward from the top of a building 60 feet tall at an initial velocity of 70 feet $p$ second. Give the function that describes the height of the rocket in terms of time $t$.

Accepted Answer

A)  $f ( t ) = - 16 t ^ { 2 } + 60 t + 70$ 
B)  $f ( t ) = - 16 t ^ { 2 } + 70 t + 60$ 
C)  $f ( t ) = 16 t ^ { 2 } + 70 t + 60$ 
D)  $f ( t ) = - 70 t ^ { 2 } + 16 t + 60$ 
A)  $f ( t ) = - 16 t ^ { 2 } + 60 t + 70$ 
B)  $f ( t ) = - 16 t ^ { 2 } + 70 t + 60$ 
C)  $f ( t ) = 16 t ^ { 2 } + 70 t + 60$ 
D)  $f ( t ) = - 70 t ^ { 2 } + 16 t + 60$

Question 13

Provide an appropriate response.
-Find a quadratic function f having x-intercepts -9 and -2 and y-intercept 6

Accepted Answer

A)  $f ( x ) = x ^ { 2 } + 5 x + 6$ 
B)  $f ( x ) = \frac { 1 } { 3 } x ^ { 2 } + \frac { 11 } { 3 } x + 6$ 
C)  $f ( x ) = \frac { 1 } { 3 } x ^ { 2 } - \frac { 11 } { 3 } x + 6$ 
D)  $f ( x ) = x ^ { 2 } + 11 x + 18$ 
A)  $f ( x ) = x ^ { 2 } + 5 x + 6$ 
B)  $f ( x ) = \frac { 1 } { 3 } x ^ { 2 } + \frac { 11 } { 3 } x + 6$ 
C)  $f ( x ) = \frac { 1 } { 3 } x ^ { 2 } - \frac { 11 } { 3 } x + 6$ 
D)  $f ( x ) = x ^ { 2 } + 11 x + 18$

Question 14

Use synthetic division to perform the division.
-$$\frac { x ^ { 3 } - x ^ { 2 } + 5 } { x + 2 }$$

Accepted Answer

A)  $x ^ { 2 } - 3 x + 6 + \frac { - 7 } { x + 2 }$ 
B)  $x ^ { 2 } + 3 x + 6 + \frac { - 7 } { x + 2 }$ 
C)  $x ^ { 2 } - 3 x + 6 + \frac { 6 } { x + 2 }$ 
D)  $x ^ { 2 } - 2 x + 6 + \frac { 6 } { x + 2 }$ 
A)  $x ^ { 2 } - 3 x + 6 + \frac { - 7 } { x + 2 }$ 
B)  $x ^ { 2 } + 3 x + 6 + \frac { - 7 } { x + 2 }$ 
C)  $x ^ { 2 } - 3 x + 6 + \frac { 6 } { x + 2 }$ 
D)  $x ^ { 2 } - 2 x + 6 + \frac { 6 } { x + 2 }$

Question 15

Given the equation or other information for a parabola, find the matching description or graph.
-$$\begin{array} { l } 
f ( x ) = a x ^ { 2 } + b x + c \
a  0
\end{array}$$

Accepted Answer

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

Question 16

Find the equation of the axis of symmetry of the parabola.
-$$y = x ^ { 2 } - 16 x + 73$$

Accepted Answer

A)  $x = 9$ 
B)  $x = 0$ 
C)  $x = - 8$ 
D)  $x = 8$ 
A)  $x = 9$ 
B)  $x = 0$ 
C)  $x = - 8$ 
D)  $x = 8$

Provide an appropriate response. -Find a quadratic function $\mathrm { f }$ having $\mathrm { x }$ -intercepts 3 and $- 4$ and $y$ -intercept $- 24$ .

Solve the problem. -The weight of a body above the surface of the earth is inversely proportional to the square of its distance from the center of the earth. What is the effect on the weight when the distance is multiplied by 4 ?

Solve the problem. -The length of a table is 11 inches more than its width. If the area of the table is 1692 square inches, what is its length?

Give the domain and range for the rational function. Use interval notation. - $f ( x ) = \frac { 1 } { ( x + 8 ) ^ { 2 } }$

Solve the problem. -If the average cost per unit $C ( x )$ to produce $x$ units of plywood is given by $C ( x ) = \frac { 300 } { x + 10 }$ , what is the unit cost for 20 units?

Provide an appropriate response. -Explain the behavior of the graph of $\mathrm { f } ( \mathrm { x } )$ as it approaches its vertical asymptote. $f ( x ) = \frac { 4 } { ( x - 8 ) ^ { 2 } }$

Express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - $f ( x ) = 3 x ^ { 4 } - 9 x ^ { 3 } + 2 x ^ { 2 } - 6 x ; \quad k = 3$

Determine which of the rational functions given below has the following feature(s). -The $y$ -intercept is 4

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $5 x ^ { 3 } + 8 x ^ { 2 } - 3 x + 2 ; x + 2$

Solve the problem. -If an object is propelled upward from a height of 160 feet at an initial velocity of 144 feet per second, then its height after $t$ seconds is given by the equation $h ( t ) = - 16 t ^ { 2 } + 144 t + 160$ . After how many seconds does the object hit the ground?

Give the equation of any oblique asymptotes. - $f ( x ) = \frac { x ^ { 2 } + 4 x + 3 } { x + 7 }$

Solve the problem. -A rock is propelled upward from the top of a building 60 feet tall at an initial velocity of 70 feet $p$ second. Give the function that describes the height of the rocket in terms of time $t$ .

Provide an appropriate response. -Find a quadratic function f having x-intercepts -9 and -2 and y-intercept 6

Use synthetic division to perform the division. - $\frac { x ^ { 3 } - x ^ { 2 } + 5 } { x + 2 }$

Given the equation or other information for a parabola, find the matching description or graph. - f(x)=a+bx+c a<0;-4ac>0

Find the equation of the axis of symmetry of the parabola. - $y = x ^ { 2 } - 16 x + 73$

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

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Further Topics in Algebra

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Exam 3: Polynomial and Rational Functions

Provide an appropriate response. -Find a quadratic function f\mathrm { f }f having x\mathrm { x }x -intercepts 3 and −4- 4−4 and yyy -intercept −24- 24−24 .