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)  $P ( x ) = x ^ { 3 } - 7 x ^ { 2 } - 13 x + 40$

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)  $f ( x ) = \frac { x - 4 } { x }$

Question 3

Sketch the graph of the parabola.
-

Accepted Answer

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)  $y = 8$

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)  $( - \infty , - 4 - \sqrt { 5 } ) \cup ( - 4 + \sqrt { 5 } , \infty )$

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)  $P ( x ) = 5 x ^ { 3 } - 15 x ^ { 2 } + 5 x - 15$

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: $( - \infty , 5 )$

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

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

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

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: $[ 5 , \infty )$

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

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)  $f ( x ) = - 2 ( x + 2 ) ^ { 2 } ( x - 1 )$

Question 15

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

Accepted Answer

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

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)

Question 19

Sketch the graph of the parabola.
-

Accepted Answer

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

Exam 3: Polynomial and Rational Functions

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $- 3,2,8$ 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. - $7 x ^ { 4 } + 13 x ^ { 3 } - 2 x ^ { 2 } + x + 4 ; x + 2$

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?

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

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?

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. - $h ( x ) = \frac { 5 } { x - 6 }$

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​

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. - $7 x ^ { 4 } + 13 x ^ { 3 } - 2 x ^ { 2 } + x + 4 ; x + 2$

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

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. - $h ( x ) = \frac { 5 } { x - 6 }$