Question 1

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
-Zeros of $- 3,2,8$ and $P ( 1 ) = 28$

Accepted Answer

A)  $P ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 13 x + 40$ 
B)  $P ( x ) = x ^ { 3 } - 7 x ^ { 2 } - 14 x + 48$ 
C)  $P ( x ) = x ^ { 3 } - 7 x ^ { 2 } - 14 x - 48$ 
D)  $P ( x ) = x ^ { 3 } - 7 x ^ { 2 } - 13 x + 40$ 
A)  $P ( x ) = x ^ { 3 } + 7 x ^ { 2 } - 13 x + 40$ 
B)  $P ( x ) = x ^ { 3 } - 7 x ^ { 2 } - 14 x + 48$ 
C)  $P ( x ) = x ^ { 3 } - 7 x ^ { 2 } - 14 x - 48$ 
D)  $P ( x ) = x ^ { 3 } - 7 x ^ { 2 } - 13 x + 40$

Question 2

Determine which of the rational functions given below has the following feature(s).
-The $x$-axis is its horizontal asymptote

Accepted Answer

A)  $f ( x ) = \frac { 9 } { x - 4 }$ 
B)  $f ( x ) = \frac { x + 4 } { x + 9 }$ 
C)  $f ( x ) = \frac { 4 x - 1 } { x + 9 }$ 
D)  $f ( x ) = \frac { x - 4 } { x }$ 
A)  $f ( x ) = \frac { 9 } { x - 4 }$ 
B)  $f ( x ) = \frac { x + 4 } { x + 9 }$ 
C)  $f ( x ) = \frac { 4 x - 1 } { x + 9 }$ 
D)  $f ( x ) = \frac { x - 4 } { x }$

Question 3

Sketch the graph of the parabola.
-

Accepted Answer

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

Question 4

Use the boundedness theorem to determine whether the statement is true or false.
-The polynomial $f ( x ) = x ^ { 4 } - 9 x ^ { 3 } - 22 x ^ { 2 }$ has no real zero greater than 8 .

Accepted Answer

A) True 
 B)False

Question 5

Give the equatiosn of any horizontal asymptotes.
-$$g ( x ) = \frac { x ^ { 2 } + 8 x - 5 } { x - 5 }$$

Accepted Answer

A)  $y = 0$ 
B)  none 
C)  $y = - 5$ 
D)  $y = 8$ 
A)  $y = 0$ 
B)  none 
C)  $y = - 5$ 
D)  $y = 8$

Question 6

Solve the inequality. Write the solution set in interval notation.
-$$- x ^ { 2 } + 8 x - 11 < 0$$

Accepted Answer

A)  $( - \infty , 4 - \sqrt { 5 } ) \cup ( 4 + \sqrt { 5 } , \infty )$ 
B)  $( - 4 - \sqrt { 5 } , - 4 + \sqrt { 5 } )$ 
C)  $( 4 - \sqrt { 5 } , 4 + \sqrt { 5 } )$ 
D)  $( - \infty , - 4 - \sqrt { 5 } ) \cup ( - 4 + \sqrt { 5 } , \infty )$ 
A)  $( - \infty , 4 - \sqrt { 5 } ) \cup ( 4 + \sqrt { 5 } , \infty )$ 
B)  $( - 4 - \sqrt { 5 } , - 4 + \sqrt { 5 } )$ 
C)  $( 4 - \sqrt { 5 } , 4 + \sqrt { 5 } )$ 
D)  $( - \infty , - 4 - \sqrt { 5 } ) \cup ( - 4 + \sqrt { 5 } , \infty )$

Question 7

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
-Zeros of $3 , i , - i$ and $P ( 2 ) = 25$

Accepted Answer

A)  $P ( x ) = - 5 x ^ { 3 } + 15 x ^ { 2 } - 5 x + 15$ 
B)  $P ( x ) = - 5 x ^ { 3 } + 15 x ^ { 2 } + 5 x - 15$ 
C)  $P ( x ) = 5 x ^ { 3 } - 15 x ^ { 2 } - 5 x + 15$ 
D)  $P ( x ) = 5 x ^ { 3 } - 15 x ^ { 2 } + 5 x - 15$ 
A)  $P ( x ) = - 5 x ^ { 3 } + 15 x ^ { 2 } - 5 x + 15$ 
B)  $P ( x ) = - 5 x ^ { 3 } + 15 x ^ { 2 } + 5 x - 15$ 
C)  $P ( x ) = 5 x ^ { 3 } - 15 x ^ { 2 } - 5 x + 15$ 
D)  $P ( x ) = 5 x ^ { 3 } - 15 x ^ { 2 } + 5 x - 15$

Question 8

Give the domain and range for the rational function. Use interval notation.
-$$f ( x ) = - \frac { 1 } { ( x - 7 ) ^ { 2 } } + 5$$

Accepted Answer

A)  Domain: $( - \infty , 7 ) \cup ( 7 , \infty )$; Range: $( - \infty , 0 )$ 
B)  Domain: $( - \infty , 7 ) \cup ( 7 , \infty )$; Range: $( - \infty , 5 )$ 
C)  Domain: $( - \infty , 7 ) \cup ( 7 , \infty )$; Range: $( 5 , \infty )$ 
D)  Domain: $( - \infty , - 7 ) \cup ( - 7 , \infty )$; Range: $( - \infty , 5 )$ 
A)  Domain: $( - \infty , 7 ) \cup ( 7 , \infty )$; Range: $( - \infty , 0 )$ 
B)  Domain: $( - \infty , 7 ) \cup ( 7 , \infty )$; Range: $( - \infty , 5 )$ 
C)  Domain: $( - \infty , 7 ) \cup ( 7 , \infty )$; Range: $( 5 , \infty )$ 
D)  Domain: $( - \infty , - 7 ) \cup ( - 7 , \infty )$; Range: $( - \infty , 5 )$

Question 9

Solve the problem.
-The intensity of a radio signal from the radio station varies inversely as the square of the distance from the station. Suppose the the intensity is 8000 units at a distance of 2 miles. What will the
Intensity be at a distance of 7 miles? Round your answer to the nearest unit.

Accepted Answer

A)  679 units 
B)  617 units 
C)  636 units 
D)  653 units 
A)  679 units 
B)  617 units 
C)  636 units 
D)  653 units

Question 10

Solve the problem.
-If $f$ varies jointly as $\mathrm { q } ^ { 2 }$ and $h$, and $f = 64$ when $q = 4$ and $h = 2$, find $f$ when $q = 2$ and $h = 5$.

Accepted Answer

A)  20 
B)  10 
C)  40 
D)  8 
A)  20 
B)  10 
C)  40 
D)  8

Question 11

Use the factor theorem to decide whether or not the second polynomial is a factor of the first.
-$$7 x ^ { 4 } + 13 x ^ { 3 } - 2 x ^ { 2 } + x + 4 ; x + 2$$

Accepted Answer

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

Question 12

Use the equation and the corresponding graph for the quadratic function to find what is requested.
-$f(x)=(x-2)^{2}-5$

Find the domain and range.

Accepted Answer

A)  Domain: $[ - 5 , \infty )$; Range: $( - \infty , \infty )$ 
B)  Domain: $( - \infty , \infty )$; Range: $( - \infty , - 5 ]$ 
C)  Domain: $( - \infty , \infty )$; Range: $[ - 5 , \infty )$ 
D)  Domain: $( - 5 , \infty )$; Range: $[ 5 , \infty )$ 
A)  Domain: $[ - 5 , \infty )$; Range: $( - \infty , \infty )$ 
B)  Domain: $( - \infty , \infty )$; Range: $( - \infty , - 5 ]$ 
C)  Domain: $( - \infty , \infty )$; Range: $[ - 5 , \infty )$ 
D)  Domain: $( - 5 , \infty )$; Range: $[ 5 , \infty )$

Question 13

Solve the problem. Round your answer to two decimal places.
-The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of
45 miles per hour?

Accepted Answer

A)  154.05 ft 
B)  141.75 ft 
C)  142.09 ft 
D)  121.5 ft 
A)  154.05 ft 
B)  141.75 ft 
C)  142.09 ft 
D)  121.5 ft

Question 14

Find a polynomial function f(x) of least possible degree having the graph shown.
-

Accepted Answer

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

Question 15

Graph the function.
-$f(x)=\frac{3}{x}-2$

Accepted Answer

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

Question 16

Write the word or phrase that best completes each statement or answers the question.
-What are the possible number of real zeros (counting multiplicities) for a polynomial
function with real coefficients of degree four?

Accepted Answer

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

Question 17

Find a polynomial function f(x) of least possible degree having the graph shown.
-

Accepted Answer

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

Question 18

Graph the polynomial function. Factor first if the expression is not in factored form.
-$f(x)=(3 x+2)(x-2)(x-1)$

Accepted Answer

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

Question 19

Sketch the graph of the parabola.
-

Accepted Answer

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

Question 20

Give the equation of any oblique asymptotes.
-$$h ( x ) = \frac { 5 } { x - 6 }$$

Accepted Answer

A)  $y = x - 6$ 
B)  $y = 6$ 
C)  $x = - 6$ 
D)  none 
A)  $y = x - 6$ 
B)  $y = 6$ 
C)  $x = - 6$ 
D)  none

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $- 3,2,8$ and $P ( 1 ) = 28$

Determine which of the rational functions given below has the following feature(s). -The $x$ -axis is its horizontal asymptote

Sketch the graph of the parabola. -

Use the boundedness theorem to determine whether the statement is true or false. -The polynomial $f ( x ) = x ^ { 4 } - 9 x ^ { 3 } - 22 x ^ { 2 }$ has no real zero greater than 8 .

Give the equatiosn of any horizontal asymptotes. - $g ( x ) = \frac { x ^ { 2 } + 8 x - 5 } { x - 5 }$

Solve the inequality. Write the solution set in interval notation. - $- x ^ { 2 } + 8 x - 11 < 0$

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $3 , i , - i$ and $P ( 2 ) = 25$

Give the domain and range for the rational function. Use interval notation. - $f ( x ) = - \frac { 1 } { ( x - 7 ) ^ { 2 } } + 5$

Solve the problem. -The intensity of a radio signal from the radio station varies inversely as the square of the distance from the station. Suppose the the intensity is 8000 units at a distance of 2 miles. What will the Intensity be at a distance of 7 miles? Round your answer to the nearest unit.

Solve the problem. -If $f$ varies jointly as $\mathrm { q } ^ { 2 }$ and $h$ , and $f = 64$ when $q = 4$ and $h = 2$ , find $f$ when $q = 2$ and $h = 5$ .

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $7 x ^ { 4 } + 13 x ^ { 3 } - 2 x ^ { 2 } + x + 4 ; x + 2$

Use the equation and the corresponding graph for the quadratic function to find what is requested. - $f(x)=(x-2)^{2}-5$ $Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=(x-2)^{2}-5 Find the domain and range.$ Find the domain and range.

Solve the problem. Round your answer to two decimal places. -The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 45 miles per hour?

Find a polynomial function f(x) of least possible degree having the graph shown. -

Graph the function. - $f(x)=\frac{3}{x}-2$ $Graph the function. - f(x)=\frac{3}{x}-2$

Write the word or phrase that best completes each statement or answers the question. -What are the possible number of real zeros (counting multiplicities) for a polynomial function with real coefficients of degree four?

Find a polynomial function f(x) of least possible degree having the graph shown. -

Graph the polynomial function. Factor first if the expression is not in factored form. - $f(x)=(3 x+2)(x-2)(x-1)$

Sketch the graph of the parabola. -

Give the equation of any oblique asymptotes. - $h ( x ) = \frac { 5 } { x - 6 }$

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

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of −3,2,8- 3,2,8−3,2,8 and P(1)=28P ( 1 ) = 28P(1)=28

Determine which of the rational functions given below has the following feature(s). -The xxx -axis is its horizontal asymptote

Sketch the graph of the parabola. -

Use the boundedness theorem to determine whether the statement is true or false. -The polynomial f(x)=x4−9x3−22x2f ( x ) = x ^ { 4 } - 9 x ^ { 3 } - 22 x ^ { 2 }f(x)=x4−9x3−22x2 has no real zero greater than 8 .

Give the equatiosn of any horizontal asymptotes. - g(x)=x2+8x−5x−5g ( x ) = \frac { x ^ { 2 } + 8 x - 5 } { x - 5 }g(x)=x−5x2+8x−5​

Solve the inequality. Write the solution set in interval notation. - −x2+8x−11<0- x ^ { 2 } + 8 x - 11 < 0−x2+8x−11<0

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of 3,i,−i3 , i , - i3,i,−i and P(2)=25P ( 2 ) = 25P(2)=25

Give the domain and range for the rational function. Use interval notation. - f(x)=−1(x−7)2+5f ( x ) = - \frac { 1 } { ( x - 7 ) ^ { 2 } } + 5f(x)=−(x−7)21​+5

Solve the problem. -The intensity of a radio signal from the radio station varies inversely as the square of the distance from the station. Suppose the the intensity is 8000 units at a distance of 2 miles. What will the Intensity be at a distance of 7 miles? Round your answer to the nearest unit.

Solve the problem. -If fff varies jointly as q2\mathrm { q } ^ { 2 }q2 and hhh , and f=64f = 64f=64 when q=4q = 4q=4 and h=2h = 2h=2 , find fff when q=2q = 2q=2 and h=5h = 5h=5 .

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - 7x4+13x3−2x2+x+4;x+27 x ^ { 4 } + 13 x ^ { 3 } - 2 x ^ { 2 } + x + 4 ; x + 27x4+13x3−2x2+x+4;x+2

Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=(x−2)2−5f(x)=(x-2)^{2}-5f(x)=(x−2)2−5 Find the domain and range.

Solve the problem. Round your answer to two decimal places. -The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes 112 feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 45 miles per hour?

Find a polynomial function f(x) of least possible degree having the graph shown. -

Graph the function. - f(x)=3x−2f(x)=\frac{3}{x}-2f(x)=x3​−2

Write the word or phrase that best completes each statement or answers the question. -What are the possible number of real zeros (counting multiplicities) for a polynomial function with real coefficients of degree four?

Find a polynomial function f(x) of least possible degree having the graph shown. -

Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=(3x+2)(x−2)(x−1)f(x)=(3 x+2)(x-2)(x-1)f(x)=(3x+2)(x−2)(x−1)

Sketch the graph of the parabola. -

Give the equation of any oblique asymptotes. - h(x)=5x−6h ( x ) = \frac { 5 } { x - 6 }h(x)=x−65​

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

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $- 3,2,8$ and $P ( 1 ) = 28$

Determine which of the rational functions given below has the following feature(s). -The $x$ -axis is its horizontal asymptote

Use the boundedness theorem to determine whether the statement is true or false. -The polynomial $f ( x ) = x ^ { 4 } - 9 x ^ { 3 } - 22 x ^ { 2 }$ has no real zero greater than 8 .

Give the equatiosn of any horizontal asymptotes. - $g ( x ) = \frac { x ^ { 2 } + 8 x - 5 } { x - 5 }$

Solve the inequality. Write the solution set in interval notation. - $- x ^ { 2 } + 8 x - 11 < 0$

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $3 , i , - i$ and $P ( 2 ) = 25$

Give the domain and range for the rational function. Use interval notation. - $f ( x ) = - \frac { 1 } { ( x - 7 ) ^ { 2 } } + 5$

Solve the problem. -If $f$ varies jointly as $\mathrm { q } ^ { 2 }$ and $h$ , and $f = 64$ when $q = 4$ and $h = 2$ , find $f$ when $q = 2$ and $h = 5$ .

Use the factor theorem to decide whether or not the second polynomial is a factor of the first. - $7 x ^ { 4 } + 13 x ^ { 3 } - 2 x ^ { 2 } + x + 4 ; x + 2$

Use the equation and the corresponding graph for the quadratic function to find what is requested. - $f(x)=(x-2)^{2}-5$ $Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=(x-2)^{2}-5 Find the domain and range.$ Find the domain and range.

Graph the function. - $f(x)=\frac{3}{x}-2$ $Graph the function. - f(x)=\frac{3}{x}-2$

Graph the polynomial function. Factor first if the expression is not in factored form. - $f(x)=(3 x+2)(x-2)(x-1)$

Give the equation of any oblique asymptotes. - $h ( x ) = \frac { 5 } { x - 6 }$