Question 1

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
-Zeros of $- 5$ and $1 - i , P ( 0 ) = 10$

Accepted Answer

A)  $P ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 8 x$ 
B)  $P ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 3 x + 5$ 
C)  $P ( x ) = x ^ { 3 } + 3 x ^ { 2 } + 8 x + 10$ 
D)  $P ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 8 x + 10$ 
A)  $P ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 8 x$ 
B)  $P ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 3 x + 5$ 
C)  $P ( x ) = x ^ { 3 } + 3 x ^ { 2 } + 8 x + 10$ 
D)  $P ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 8 x + 10$

Question 2

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope
positive or negative. If quadratic, decide whether the leading coefficient a of xS1U1P12S1S1P0 should be positive or negative.
-

Accepted Answer

A)  quadratic; negative 
B)  linear; negative 
C)  quadratic; positive 
D)  linear; positive 
A)  quadratic; negative 
B)  linear; negative 
C)  quadratic; positive 
D)  linear; positive

Question 3

Answer the question
-What type of variation is suggested by the graph?

Accepted Answer

A)  $y$ varies inversely as the square of $x$ 
B)  $x$ varies inversely as the square of $y$ 
C)  $y$ varies directly as the square of $x$ 
D)  $x$ varies directly as the square of $y$ 
A)  $y$ varies inversely as the square of $x$ 
B)  $x$ varies inversely as the square of $y$ 
C)  $y$ varies directly as the square of $x$ 
D)  $x$ varies directly as the square of $y$

Question 4

Find all rational zeros and factor f(x).
-$$f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - 27 x - 90$$

Accepted Answer

A)  $4,6 , - 10 ; f ( x ) = ( x - 4 ) ( x - 6 ) ( x + 10 )$ 
B)  $- 4 , - 6,10 ; f ( x ) = ( x + 4 ) ( x + 6 ) ( x - 10 )$ 
C)  $- 3 , - 6,5 ; f ( x ) = ( x + 3 ) ( x + 6 ) ( x - 5 )$ 
D)  $3,6 , - 5 ; f ( x ) = ( x - 3 ) ( x - 6 ) ( x + 5 )$ 
A)  $4,6 , - 10 ; f ( x ) = ( x - 4 ) ( x - 6 ) ( x + 10 )$ 
B)  $- 4 , - 6,10 ; f ( x ) = ( x + 4 ) ( x + 6 ) ( x - 10 )$ 
C)  $- 3 , - 6,5 ; f ( x ) = ( x + 3 ) ( x + 6 ) ( x - 5 )$ 
D)  $3,6 , - 5 ; f ( x ) = ( x - 3 ) ( x - 6 ) ( x + 5 )$

Question 5

Solve the problem. Round your answer to two decimal places.
-The distance an object falls when dropped from a tower varies directly as the square of the time it falls. If the object falls 144 feet in 3 seconds, how far will it fall in 4 seconds?

Accepted Answer

A)  256 ft 
B)  224 ft 
C)  288 ft 
D)  64 ft 
A)  256 ft 
B)  224 ft 
C)  288 ft 
D)  64 ft

Question 6

Use the remainder theorem and synthetic division to find f(k).
-$$k = 2 ; f ( x ) = x ^ { 6 } - 2 x ^ { 5 } - 2 x ^ { 4 } + 2 x ^ { 3 } - 3 x ^ { 2 } - 3 x - 6$$

Accepted Answer

A)  $- 40$ 
B)  $- 39$ 
C)  68 
D)  40 
A)  $- 40$ 
B)  $- 39$ 
C)  68 
D)  40

Question 7

Provide an appropriate response.
-A quadratic equation f(x) = 0 has a solution x = 3. Its graph has vertex (-1, -16). What is the other solution of the equation?

Accepted Answer

A)  -4 
B) -5 
C) -3 
D) 7 
A)  -4 
B) -5 
C) -3 
D) 7

Question 8

Give the equation of any oblique asymptotes.
-$$f ( x ) = \frac { 9 x ^ { 2 } } { 5 x ^ { 2 } + 9 }$$

Accepted Answer

A)  $y = x + 9$ 
B)  $y = x + \frac { 9 } { 5 }$ 
C)  none 
D)  $x = y + 9$ 
A)  $y = x + 9$ 
B)  $y = x + \frac { 9 } { 5 }$ 
C)  none 
D)  $x = y + 9$

Question 9

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
-Zeros of 4 and i, $\mathrm { P } ( 1 ) = - 6$

Accepted Answer

A)  $P ( x ) = x ^ { 3 } + 4 x ^ { 2 } + x - 4$ 
B)  $P ( x ) = x ^ { 3 } - 4 x ^ { 2 } + x + 4$ 
C)  $P ( x ) = x ^ { 3 } + 4 x ^ { 2 } - x + 4$ 
D)  $P ( x ) = x ^ { 3 } - 4 x ^ { 2 } + x - 4$ 
A)  $P ( x ) = x ^ { 3 } + 4 x ^ { 2 } + x - 4$ 
B)  $P ( x ) = x ^ { 3 } - 4 x ^ { 2 } + x + 4$ 
C)  $P ( x ) = x ^ { 3 } + 4 x ^ { 2 } - x + 4$ 
D)  $P ( x ) = x ^ { 3 } - 4 x ^ { 2 } + x - 4$

Question 10

Use the graph to answer the question.
-Find the horizontal and vertical asymptotes of the rational function graphed below.

Accepted Answer

A)  Horizontal: $y = \pm 1$; vertical: $x = 3$ 
B)  Horizontal: $y = 3$; vertical: $x = \pm 1$ 
C)  Horizontal: none; vertical: $x = \pm 1$ 
D)  Horizontal: $\mathrm { y } = 0$; vertical: $\mathrm { x } = \pm 1$ 
A)  Horizontal: $y = \pm 1$; vertical: $x = 3$ 
B)  Horizontal: $y = 3$; vertical: $x = \pm 1$ 
C)  Horizontal: none; vertical: $x = \pm 1$ 
D)  Horizontal: $\mathrm { y } = 0$; vertical: $\mathrm { x } = \pm 1$

Question 11

Write the word or phrase that best completes each statement or answers the question.
-Why is it not possible for a function defined by a polynomial of degree 4 with real
coefficients to have zeros of 2, 3, 5, and 1 + i?

Accepted Answer

By the Conjugate zeros Theorem

Question 12

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary.
-$$f ( x ) = x ^ { 4 } - 5 x ^ { 2 } - 36$$

Accepted Answer

A)  $- 2 i , 2 i , 3 i , - 3 i$ 
B)  $- 2 i , 2 i , 6 , - 6$ 
C)  $- 2 i , 2 i , 3 , - 3$ 
D)  $- 2 i , 2 i , 6 i , - 6 i$ 
A)  $- 2 i , 2 i , 3 i , - 3 i$ 
B)  $- 2 i , 2 i , 6 , - 6$ 
C)  $- 2 i , 2 i , 3 , - 3$ 
D)  $- 2 i , 2 i , 6 i , - 6 i$

Question 13

Solve the problem.
-Suppose a cost-benefit model is given by $f ( x ) = \frac { 2.8 x } { 100 - x }$, where $y$ is the cost in thousands of dollars for removing x percent of a given pollutant. Find the cost of removing $80 \%$ to the nearest dollar.

Accepted Answer

A)  $\$ 2240$ 
B)  $\$ 11,200$ 
C)  $\$ 4000$ 
D)  $\$ 2800$ 
A)  $\$ 2240$ 
B)  $\$ 11,200$ 
C)  $\$ 4000$ 
D)  $\$ 2800$

Question 14

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

Accepted Answer

A)  $f ( x ) = ( x + 2 ) \left( 3 x ^ { 2 } - 4 x + 2 \right) + 18$ 
B)  $f ( x ) = ( x + 2 ) \left( x ^ { 2 } - 3 x + 6 \right) - 6$ 
C)  $f ( x ) = ( x + 2 ) \left( x ^ { 2 } + x + 2 \right) + 10$ 
D)  $f ( x ) = ( x + 2 ) \left( x ^ { 2 } - 3 x + 6 \right) + 6$ 
A)  $f ( x ) = ( x + 2 ) \left( 3 x ^ { 2 } - 4 x + 2 \right) + 18$ 
B)  $f ( x ) = ( x + 2 ) \left( x ^ { 2 } - 3 x + 6 \right) - 6$ 
C)  $f ( x ) = ( x + 2 ) \left( x ^ { 2 } + x + 2 \right) + 10$ 
D)  $f ( x ) = ( x + 2 ) \left( x ^ { 2 } - 3 x + 6 \right) + 6$

Question 15

Solve the problem.
-The area of a square is numerically 12 more than the perimeter. Find the length of the side.

Accepted Answer

A)  18 units 
B)  24 units 
C)  6 units 
D)  72 units 
A)  18 units 
B)  24 units 
C)  6 units 
D)  72 units

Question 16

Solve the problem.
-If s varies directly as t2, and s = 320 when t = 8, find s when t is 5.

Accepted Answer

A)  125 
B)  40 
C)  60 
D)  200 
A)  125 
B)  40 
C)  60 
D)  200

Question 17

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

Accepted Answer

A)  $f ( x ) = 7 ( x + 1 ) ^ { 2 } ( x - 1 ) ^ { 2 }$ 
B)  $f ( x ) = - 7 ( x + 1 ) ^ { 2 } ( x - 1 ) ^ { 2 }$ 
C)  $f ( x ) = 7 ( x + 1 ) ( x - 1 )$ 
D)  $f ( x ) = - 7 ( x + 1 ) ( x - 1 )$ 
A)  $f ( x ) = 7 ( x + 1 ) ^ { 2 } ( x - 1 ) ^ { 2 }$ 
B)  $f ( x ) = - 7 ( x + 1 ) ^ { 2 } ( x - 1 ) ^ { 2 }$ 
C)  $f ( x ) = 7 ( x + 1 ) ( x - 1 )$ 
D)  $f ( x ) = - 7 ( x + 1 ) ( x - 1 )$

Question 18

Use a graphing calculator to find the coordinates of the turning points of the graph of the polynomial function in the
indicated domain interval. Give answers to the nearest hundredth.
-$$f ( x ) = - x ^ { 4 } + 29 x ^ { 2 } - 100 ; [ 3,4 ]$$

Accepted Answer

A)  $( 3.81,110.25 )$ 
B)  $( 5,887.50 )$ 
C)  $( - 4,110.25 )$ 
D)  $( 0,100 )$ 
A)  $( 3.81,110.25 )$ 
B)  $( 5,887.50 )$ 
C)  $( - 4,110.25 )$ 
D)  $( 0,100 )$

Question 19

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

Accepted Answer

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

Question 20

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope
positive or negative. If quadratic, decide whether the leading coefficient a of xS1U1P12S1S1P0 should be positive or negative.
-

Accepted Answer

A)  quadratic; positive 
B)  linear; positive 
C)  linear; negative 
D)  quadratic; negative 
A)  quadratic; positive 
B)  linear; positive 
C)  linear; negative 
D)  quadratic; negative

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of $- 5$ and $1 - i , P ( 0 ) = 10$

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope positive or negative. If quadratic, decide whether the leading coefficient a of x² should be positive or negative. -

Answer the question -What type of variation is suggested by the graph?

Find all rational zeros and factor f(x). - $f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - 27 x - 90$

Solve the problem. Round your answer to two decimal places. -The distance an object falls when dropped from a tower varies directly as the square of the time it falls. If the object falls 144 feet in 3 seconds, how far will it fall in 4 seconds?

Use the remainder theorem and synthetic division to find f(k). - $k = 2 ; f ( x ) = x ^ { 6 } - 2 x ^ { 5 } - 2 x ^ { 4 } + 2 x ^ { 3 } - 3 x ^ { 2 } - 3 x - 6$

Provide an appropriate response. -A quadratic equation f(x) = 0 has a solution x = 3. Its graph has vertex (-1, -16). What is the other solution of the equation?

Give the equation of any oblique asymptotes. - $f ( x ) = \frac { 9 x ^ { 2 } } { 5 x ^ { 2 } + 9 }$

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of 4 and i, $\mathrm { P } ( 1 ) = - 6$

Use the graph to answer the question. -Find the horizontal and vertical asymptotes of the rational function graphed below.

Write the word or phrase that best completes each statement or answers the question. -Why is it not possible for a function defined by a polynomial of degree 4 with real coefficients to have zeros of 2, 3, 5, and 1 + i?

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 4 } - 5 x ^ { 2 } - 36$

Solve the problem. -Suppose a cost-benefit model is given by $f ( x ) = \frac { 2.8 x } { 100 - x }$ , where $y$ is the cost in thousands of dollars for removing x percent of a given pollutant. Find the cost of removing $80 \%$ to the nearest dollar.

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

Solve the problem. -The area of a square is numerically 12 more than the perimeter. Find the length of the side.

Solve the problem. -If s varies directly as t2, and s = 320 when t = 8, find s when t is 5.

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

Use a graphing calculator to find the coordinates of the turning points of the graph of the polynomial function in the indicated domain interval. Give answers to the nearest hundredth. - $f ( x ) = - x ^ { 4 } + 29 x ^ { 2 } - 100 ; [ 3,4 ]$

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

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope positive or negative. If quadratic, decide whether the leading coefficient a of x² should be positive or negative. -

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 −5- 5−5 and 1−i,P(0)=101 - i , P ( 0 ) = 101−i,P(0)=10

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope positive or negative. If quadratic, decide whether the leading coefficient a of x2 should be positive or negative. -

Answer the question -What type of variation is suggested by the graph?

Find all rational zeros and factor f(x). - f(x)=x3+4x2−27x−90f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - 27 x - 90f(x)=x3+4x2−27x−90

Solve the problem. Round your answer to two decimal places. -The distance an object falls when dropped from a tower varies directly as the square of the time it falls. If the object falls 144 feet in 3 seconds, how far will it fall in 4 seconds?

Use the remainder theorem and synthetic division to find f(k). - k=2;f(x)=x6−2x5−2x4+2x3−3x2−3x−6k = 2 ; f ( x ) = x ^ { 6 } - 2 x ^ { 5 } - 2 x ^ { 4 } + 2 x ^ { 3 } - 3 x ^ { 2 } - 3 x - 6k=2;f(x)=x6−2x5−2x4+2x3−3x2−3x−6

Provide an appropriate response. -A quadratic equation f(x) = 0 has a solution x = 3. Its graph has vertex (-1, -16). What is the other solution of the equation?

Give the equation of any oblique asymptotes. - f(x)=9x25x2+9f ( x ) = \frac { 9 x ^ { 2 } } { 5 x ^ { 2 } + 9 }f(x)=5x2+99x2​

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of 4 and i, P(1)=−6\mathrm { P } ( 1 ) = - 6P(1)=−6

Use the graph to answer the question. -Find the horizontal and vertical asymptotes of the rational function graphed below.

Write the word or phrase that best completes each statement or answers the question. -Why is it not possible for a function defined by a polynomial of degree 4 with real coefficients to have zeros of 2, 3, 5, and 1 + i?

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - f(x)=x4−5x2−36f ( x ) = x ^ { 4 } - 5 x ^ { 2 } - 36f(x)=x4−5x2−36

Solve the problem. -Suppose a cost-benefit model is given by f(x)=2.8x100−xf ( x ) = \frac { 2.8 x } { 100 - x }f(x)=100−x2.8x​ , where yyy is the cost in thousands of dollars for removing x percent of a given pollutant. Find the cost of removing 80%80 \%80% to the nearest dollar.

Express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - f(x)=x3−x2+6;k=−2f ( x ) = x ^ { 3 } - x ^ { 2 } + 6 ; k = - 2f(x)=x3−x2+6;k=−2

Solve the problem. -The area of a square is numerically 12 more than the perimeter. Find the length of the side.

Solve the problem. -If s varies directly as t2, and s = 320 when t = 8, find s when t is 5.

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

Use a graphing calculator to find the coordinates of the turning points of the graph of the polynomial function in the indicated domain interval. Give answers to the nearest hundredth. - f(x)=−x4+29x2−100;[3,4]f ( x ) = - x ^ { 4 } + 29 x ^ { 2 } - 100 ; [ 3,4 ]f(x)=−x4+29x2−100;[3,4]

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

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope positive or negative. If quadratic, decide whether the leading coefficient a of x2 should be positive or negative. -

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 $- 5$ and $1 - i , P ( 0 ) = 10$

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope positive or negative. If quadratic, decide whether the leading coefficient a of x² should be positive or negative. -

Find all rational zeros and factor f(x). - $f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - 27 x - 90$

Use the remainder theorem and synthetic division to find f(k). - $k = 2 ; f ( x ) = x ^ { 6 } - 2 x ^ { 5 } - 2 x ^ { 4 } + 2 x ^ { 3 } - 3 x ^ { 2 } - 3 x - 6$

Give the equation of any oblique asymptotes. - $f ( x ) = \frac { 9 x ^ { 2 } } { 5 x ^ { 2 } + 9 }$

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros of 4 and i, $\mathrm { P } ( 1 ) = - 6$

Find all complex zeros of the polynomial function. Give exact values. List multiple zeros as necessary. - $f ( x ) = x ^ { 4 } - 5 x ^ { 2 } - 36$

Solve the problem. -Suppose a cost-benefit model is given by $f ( x ) = \frac { 2.8 x } { 100 - x }$ , where $y$ is the cost in thousands of dollars for removing x percent of a given pollutant. Find the cost of removing $80 \%$ to the nearest dollar.

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

Use a graphing calculator to find the coordinates of the turning points of the graph of the polynomial function in the indicated domain interval. Give answers to the nearest hundredth. - $f ( x ) = - x ^ { 4 } + 29 x ^ { 2 } - 100 ; [ 3,4 ]$

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

Tell whether a linear model or a quadratic model is appropriate for the data. If linear, tell whether the slope positive or negative. If quadratic, decide whether the leading coefficient a of x² should be positive or negative. -