Question 1

Solve the problem.
-$f(x)=x^{3}+2$

Accepted Answer

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

Question 2

For the polynomial, one zero is given. Find all others.
-$$P ( x ) = x ^ { 4 } - 8 x ^ { 3 } + 14 x ^ { 2 } - 8 x + 13 ; i$$

Accepted Answer

A)  $- i , - 4 + \sqrt { 3 } , - 4 - \sqrt { 3 }$ 
B)  $- \mathrm { i } , 1 + \sqrt { 3 } , 1 - \sqrt { 3 }$ 
C)  $- \mathrm { i } , 4 + 2 \sqrt { 3 } , 4 - 2 \sqrt { 3 }$ 
D)  $- \mathrm { i } , 4 + \sqrt { 3 } , 4 - \sqrt { 3 }$ 
A)  $- i , - 4 + \sqrt { 3 } , - 4 - \sqrt { 3 }$ 
B)  $- \mathrm { i } , 1 + \sqrt { 3 } , 1 - \sqrt { 3 }$ 
C)  $- \mathrm { i } , 4 + 2 \sqrt { 3 } , 4 - 2 \sqrt { 3 }$ 
D)  $- \mathrm { i } , 4 + \sqrt { 3 } , 4 - \sqrt { 3 }$

Question 3

Solve the problem.
-Your company uses the quadratic model $y = - 11 x ^ { 2 } + 350 x$ to represent how many units ( $y$ ) of a new product will be sold (x) weeks after its release. How many units can you expect to sell in week 12?

Accepted Answer

A)  5784 units 
B)  4068 units 
C)  2616 units 
D)  4332 units 
A)  5784 units 
B)  4068 units 
C)  2616 units 
D)  4332 units

Question 4

Solve the problem.
-A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 12 feet by 15 feet and the area of the rug is 108 square feet, how wide will the border be?

Accepted Answer

A)  $2.2 \mathrm { ft }$ 
B)  $3 \mathrm { ft }$ 
C)  $1 \mathrm { ft }$ 
D)  $1.5 \mathrm { ft }$ 
A)  $2.2 \mathrm { ft }$ 
B)  $3 \mathrm { ft }$ 
C)  $1 \mathrm { ft }$ 
D)  $1.5 \mathrm { ft }$

Question 5

Write the word or phrase that best completes each statement or answers the question.
-Find an equation for a rational function with the following asymptotes: vertical asymptote $x = 7$, horizontal asymptote $y = 8$

Accepted Answer

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

Question 6

Use the boundedness theorem to determine whether the statement is true or false.
-The polynomial $f ( x ) = x ^ { 4 } - x ^ { 3 } + 2 x ^ { 2 } - 4 x - 10$ has no real zero greater than 3 .

Accepted Answer

A) True 
 B)False

Question 7

Find all rational zeros and factor f(x).
-$$f ( x ) = 10 x ^ { 3 } + 53 x ^ { 2 } + 14 x - 5$$

Accepted Answer

A)  $- \frac { 1 } { 10 } , 1 , - 5 ; f ( x ) = ( 10 x + 1 ) ( x - 1 ) ( x + 5 )$ 
B)  $- 2,5 , - 5 ; f ( x ) = ( x + 2 ) ( x - 5 ) ( x + 5 )$ 
C)  $- \frac { 1 } { 2 } , \frac { 1 } { 5 } , - 5 ; f ( x ) = ( 2 x + 1 ) ( 5 x - 1 ) ( x + 5 )$ 
D)  $- 2,5 , - 5 ; f ( x ) = ( 2 x + 1 ) ( 5 x - 1 ) ( x + 5 )$ 
A)  $- \frac { 1 } { 10 } , 1 , - 5 ; f ( x ) = ( 10 x + 1 ) ( x - 1 ) ( x + 5 )$ 
B)  $- 2,5 , - 5 ; f ( x ) = ( x + 2 ) ( x - 5 ) ( x + 5 )$ 
C)  $- \frac { 1 } { 2 } , \frac { 1 } { 5 } , - 5 ; f ( x ) = ( 2 x + 1 ) ( 5 x - 1 ) ( x + 5 )$ 
D)  $- 2,5 , - 5 ; f ( x ) = ( 2 x + 1 ) ( 5 x - 1 ) ( x + 5 )$

Question 8

Solve the problem. Round to the nearest tenth unless indicated otherwise.
-The resistance of a wire varies directly as the length of the wire and inversely as the square of the diameter of the wire. A 20 foot length of wire with a diameter of 0.1 inch has a resistance of
3 ohms. What would the resistance be for a 48 foot length, with diameter 0.01 inch, of the same
Kind of wire ?

Accepted Answer

A)  720 ohms 
B)  717.5 ohms 
C)  713 ohms 
D)  732 ohms 
A)  720 ohms 
B)  717.5 ohms 
C)  713 ohms 
D)  732 ohms

Question 9

Solve the inequality. Write the solution set in interval notation.
-$$x ^ { 2 } - 5 x - 14 > 0$$

Accepted Answer

A)  $( - \infty , - 2 ) \cup ( 7 , \infty )$ 
B)  $( - 7,2 )$ 
C)  $( - 2,7 )$ 
D)  $( - \infty , - 7 )$ 
A)  $( - \infty , - 2 ) \cup ( 7 , \infty )$ 
B)  $( - 7,2 )$ 
C)  $( - 2,7 )$ 
D)  $( - \infty , - 7 )$

Question 10

Answer the question
-If y varies directly as the square of x, and x is doubled, how is y changed?

Accepted Answer

A)  y is twice as large as before 
B)  y is four times as large as before 
C)  y is half as large as before 
D)  y is one-quarter as large as before 
A)  y is twice as large as before 
B)  y is four times as large as before 
C)  y is half as large as before 
D)  y is one-quarter as large as before

Question 11

Solve the problem.
-$f(x)=x^{3}+4$

Accepted Answer

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

Question 12

Determine which of the rational functions given below has the following feature(s).
-The horizontal asymptote is $\mathrm { y } = 5$

Accepted Answer

A)  $f ( x ) = \frac { x + 5 } { x + 9 }$ 
B)  $f ( x ) = \frac { 5 x ^ { 2 } - 1 } { x + 9 }$ 
C)  $f ( x ) = \frac { 5 x - 1 } { x + 9 }$ 
D)  $f ( x ) = \frac { 5 } { x - 5 }$ 
A)  $f ( x ) = \frac { x + 5 } { x + 9 }$ 
B)  $f ( x ) = \frac { 5 x ^ { 2 } - 1 } { x + 9 }$ 
C)  $f ( x ) = \frac { 5 x - 1 } { x + 9 }$ 
D)  $f ( x ) = \frac { 5 } { x - 5 }$

Question 13

Give the equatiosn of any horizontal asymptotes.
-$$h ( x ) = \frac { 5 x ^ { 2 } } { 5 x ^ { 2 } - 7 }$$

Accepted Answer

A)  none 
B)  $y = 7$ 
C)  $y = \sqrt { 7 }$ 
D)  $y = 1$ 
A)  none 
B)  $y = 7$ 
C)  $y = \sqrt { 7 }$ 
D)  $y = 1$

Question 14

Match the equation to the correct graph.
-$$y = - ( x + 7 ) ^ { 2 } + 5$$

Accepted Answer

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

Question 15

Match the equation to the correct graph.
-$$y = - ( x + 6 ) ^ { 2 } + 5$$

Accepted Answer

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

Question 16

Solve.
-The population of a city has varied considerably in recent years. The data in the table relates the population $P$ to time $t$, in years. Use a quadratic function fitted to the data to predict the population in year $10 .$

Accepted Answer

A)  58,964 
B)  119,000 
C)  48,431 
D)  81,020 
A)  58,964 
B)  119,000 
C)  48,431 
D)  81,020

Question 17

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary.
-$$f ( x ) = x ^ { 4 } - 9$$

Accepted Answer

A)  $\sqrt { 3 } , - \sqrt { 3 } , 3 i , - 3 i$ 
B)  $\sqrt { 3 } , \sqrt { 3 } i$ 
C)  $\sqrt { 3 } , - \sqrt { 3 }$ 
D)  $\sqrt { 3 } , - \sqrt { 3 } i , \sqrt { 3 } i , - \sqrt { 3 }$ 
A)  $\sqrt { 3 } , - \sqrt { 3 } , 3 i , - 3 i$ 
B)  $\sqrt { 3 } , \sqrt { 3 } i$ 
C)  $\sqrt { 3 } , - \sqrt { 3 }$ 
D)  $\sqrt { 3 } , - \sqrt { 3 } i , \sqrt { 3 } i , - \sqrt { 3 }$

Question 18

Solve the problem.
-$f(x)=-\frac{1}{3}(x-5)^{2}$

Accepted Answer

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

Question 19

Sketch the graph of the parabola.
-$y=-\frac{4}{7}(x-7)^{2}+4$

Accepted Answer

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

Question 20

Use the factor theorem to decide whether or not the second polynomial is a factor of the first.
-$2 x ^ { 2 } - 19 x + 44 ; x - 4$

Accepted Answer

A)  Yes 
B)  $\mathrm { No }$ 
A)  Yes 
B)  $\mathrm { No }$

Solve the problem. - $f(x)=x^{3}+2$ $Solve the problem. - f(x)=x^{3}+2$

For the polynomial, one zero is given. Find all others. - $P ( x ) = x ^ { 4 } - 8 x ^ { 3 } + 14 x ^ { 2 } - 8 x + 13 ; i$

Solve the problem. -Your company uses the quadratic model $y = - 11 x ^ { 2 } + 350 x$ to represent how many units ( $y$ ) of a new product will be sold (x) weeks after its release. How many units can you expect to sell in week 12?

Solve the problem. -A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 12 feet by 15 feet and the area of the rug is 108 square feet, how wide will the border be?

Write the word or phrase that best completes each statement or answers the question. -Find an equation for a rational function with the following asymptotes: vertical asymptote $x = 7$ , horizontal asymptote $y = 8$

Use the boundedness theorem to determine whether the statement is true or false. -The polynomial $f ( x ) = x ^ { 4 } - x ^ { 3 } + 2 x ^ { 2 } - 4 x - 10$ has no real zero greater than 3 .

Find all rational zeros and factor f(x). - $f ( x ) = 10 x ^ { 3 } + 53 x ^ { 2 } + 14 x - 5$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 2 } - 5 x - 14 > 0$

Answer the question -If y varies directly as the square of x, and x is doubled, how is y changed?

Solve the problem. - $f(x)=x^{3}+4$ $Solve the problem. - f(x)=x^{3}+4$

Determine which of the rational functions given below has the following feature(s). -The horizontal asymptote is $\mathrm { y } = 5$

Give the equatiosn of any horizontal asymptotes. - $h ( x ) = \frac { 5 x ^ { 2 } } { 5 x ^ { 2 } - 7 }$

Match the equation to the correct graph. - $y = - ( x + 7 ) ^ { 2 } + 5$

Match the equation to the correct graph. - $y = - ( x + 6 ) ^ { 2 } + 5$

Solve. -The population of a city has varied considerably in recent years. The data in the table relates the population $P$ to time $t$ , in years. Use a quadratic function fitted to the data to predict the population in year $10 .$

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 4 } - 9$

Solve the problem. - $f(x)=-\frac{1}{3}(x-5)^{2}$ $Solve the problem. - f(x)=-\frac{1}{3}(x-5)^{2}$

Sketch the graph of the parabola. - $y=-\frac{4}{7}(x-7)^{2}+4$ $Sketch the graph of the parabola. - y=-\frac{4}{7}(x-7)^{2}+4$

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $2 x ^ { 2 } - 19 x + 44 ; x - 4$

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

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Exam 3: Polynomial and Rational Functions

Solve the problem. - f(x)=x3+2f(x)=x^{3}+2f(x)=x3+2

For the polynomial, one zero is given. Find all others. - P(x)=x4−8x3+14x2−8x+13;iP ( x ) = x ^ { 4 } - 8 x ^ { 3 } + 14 x ^ { 2 } - 8 x + 13 ; iP(x)=x4−8x3+14x2−8x+13;i

Solve the problem. -Your company uses the quadratic model y=−11x2+350xy = - 11 x ^ { 2 } + 350 xy=−11x2+350x to represent how many units ( yyy ) of a new product will be sold (x) weeks after its release. How many units can you expect to sell in week 12?

Solve the problem. -A rug is to fit in a room so that a border of even width is left on all four sides. If the room is 12 feet by 15 feet and the area of the rug is 108 square feet, how wide will the border be?

Write the word or phrase that best completes each statement or answers the question. -Find an equation for a rational function with the following asymptotes: vertical asymptote x=7x = 7x=7 , horizontal asymptote y=8y = 8y=8

Use the boundedness theorem to determine whether the statement is true or false. -The polynomial f(x)=x4−x3+2x2−4x−10f ( x ) = x ^ { 4 } - x ^ { 3 } + 2 x ^ { 2 } - 4 x - 10f(x)=x4−x3+2x2−4x−10 has no real zero greater than 3 .

Find all rational zeros and factor f(x). - f(x)=10x3+53x2+14x−5f ( x ) = 10 x ^ { 3 } + 53 x ^ { 2 } + 14 x - 5f(x)=10x3+53x2+14x−5

Solve the inequality. Write the solution set in interval notation. - x2−5x−14>0x ^ { 2 } - 5 x - 14 > 0x2−5x−14>0

Answer the question -If y varies directly as the square of x, and x is doubled, how is y changed?

Solve the problem. - f(x)=x3+4f(x)=x^{3}+4f(x)=x3+4

Determine which of the rational functions given below has the following feature(s). -The horizontal asymptote is y=5\mathrm { y } = 5y=5

Give the equatiosn of any horizontal asymptotes. - h(x)=5x25x2−7h ( x ) = \frac { 5 x ^ { 2 } } { 5 x ^ { 2 } - 7 }h(x)=5x2−75x2​

Match the equation to the correct graph. - y=−(x+7)2+5y = - ( x + 7 ) ^ { 2 } + 5y=−(x+7)2+5

Match the equation to the correct graph. - y=−(x+6)2+5y = - ( x + 6 ) ^ { 2 } + 5y=−(x+6)2+5

Solve. -The population of a city has varied considerably in recent years. The data in the table relates the population PPP to time ttt , in years. Use a quadratic function fitted to the data to predict the population in year 10.10 .10.

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - f(x)=x4−9f ( x ) = x ^ { 4 } - 9f(x)=x4−9

Solve the problem. - f(x)=−13(x−5)2f(x)=-\frac{1}{3}(x-5)^{2}f(x)=−31​(x−5)2

Sketch the graph of the parabola. - y=−47(x−7)2+4y=-\frac{4}{7}(x-7)^{2}+4y=−74​(x−7)2+4

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - 2x2−19x+44;x−42 x ^ { 2 } - 19 x + 44 ; x - 42x2−19x+44;x−4

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

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Review of Basic Concepts

Filters

Solve the problem. - $f(x)=x^{3}+2$ $Solve the problem. - f(x)=x^{3}+2$

For the polynomial, one zero is given. Find all others. - $P ( x ) = x ^ { 4 } - 8 x ^ { 3 } + 14 x ^ { 2 } - 8 x + 13 ; i$

Solve the problem. -Your company uses the quadratic model $y = - 11 x ^ { 2 } + 350 x$ to represent how many units ( $y$ ) of a new product will be sold (x) weeks after its release. How many units can you expect to sell in week 12?

Write the word or phrase that best completes each statement or answers the question. -Find an equation for a rational function with the following asymptotes: vertical asymptote $x = 7$ , horizontal asymptote $y = 8$

Use the boundedness theorem to determine whether the statement is true or false. -The polynomial $f ( x ) = x ^ { 4 } - x ^ { 3 } + 2 x ^ { 2 } - 4 x - 10$ has no real zero greater than 3 .

Find all rational zeros and factor f(x). - $f ( x ) = 10 x ^ { 3 } + 53 x ^ { 2 } + 14 x - 5$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 2 } - 5 x - 14 > 0$

Solve the problem. - $f(x)=x^{3}+4$ $Solve the problem. - f(x)=x^{3}+4$

Determine which of the rational functions given below has the following feature(s). -The horizontal asymptote is $\mathrm { y } = 5$

Give the equatiosn of any horizontal asymptotes. - $h ( x ) = \frac { 5 x ^ { 2 } } { 5 x ^ { 2 } - 7 }$

Match the equation to the correct graph. - $y = - ( x + 7 ) ^ { 2 } + 5$

Match the equation to the correct graph. - $y = - ( x + 6 ) ^ { 2 } + 5$

Solve. -The population of a city has varied considerably in recent years. The data in the table relates the population $P$ to time $t$ , in years. Use a quadratic function fitted to the data to predict the population in year $10 .$

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 4 } - 9$

Solve the problem. - $f(x)=-\frac{1}{3}(x-5)^{2}$ $Solve the problem. - f(x)=-\frac{1}{3}(x-5)^{2}$

Sketch the graph of the parabola. - $y=-\frac{4}{7}(x-7)^{2}+4$ $Sketch the graph of the parabola. - y=-\frac{4}{7}(x-7)^{2}+4$

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $2 x ^ { 2 } - 19 x + 44 ; x - 4$