Question 1

Find the requested function.
-Find the polynomial function with leading coefficient 6 ; degree 3 ; and $- 3,4$, and $- 4$ as zeros.

Accepted Answer

A)  $f ( x ) = ( x + 3 ) ( x - 4 ) ( x + 4 )$ 
B)  $f ( x ) = 6 ( x - 3 ) ( x + 4 ) ( x - 4 )$ 
C)  $f ( x ) = 6 ( x + 3 ) ( x - 4 ) ( x + 4 )$ 
D)  $f ( x ) = ( x - 3 ) ( x + 4 ) ( x - 4 )$ 
A)  $f ( x ) = ( x + 3 ) ( x - 4 ) ( x + 4 )$ 
B)  $f ( x ) = 6 ( x - 3 ) ( x + 4 ) ( x - 4 )$ 
C)  $f ( x ) = 6 ( x + 3 ) ( x - 4 ) ( x + 4 )$ 
D)  $f ( x ) = ( x - 3 ) ( x + 4 ) ( x - 4 )$

Question 2

Find the zeros of the function.
-$$f ( x ) = x ^ { 3 } + 12 x ^ { 2 } + 41 x + 42$$

Accepted Answer

A)  $- 2 , - 3$, and $- 7$ 
B)  2,3 , and 7 
C)  $- 1 , - 3$, and $- 7$ 
D)  $0,2,3$, and 7 
A)  $- 2 , - 3$, and $- 7$ 
B)  2,3 , and 7 
C)  $- 1 , - 3$, and $- 7$ 
D)  $0,2,3$, and 7

Question 3

Find the vertex of the graph of the function.
-$$f ( x ) = 6 x ^ { 2 } - 84 x + 304$$

Accepted Answer

A)  $( 10,7 )$ 
B)  $( 7,0 )$ 
C)  $( 10,0 )$ 
D)  $( 7,10 )$ 
A)  $( 10,7 )$ 
B)  $( 7,0 )$ 
C)  $( 10,0 )$ 
D)  $( 7,10 )$

Question 4

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the
polynomial in standard form.
-$- 1$ and $3 + 5 \mathrm { i }$

Accepted Answer

A)  $f ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 28 x + 35$ 
B)  $f ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 28 x + 34$ 
C)  $f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 28 x + 34$ 
D)  $f ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 28 x - 34$ 
A)  $f ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 28 x + 35$ 
B)  $f ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 28 x + 34$ 
C)  $f ( x ) = x ^ { 3 } + 5 x ^ { 2 } + 28 x + 34$ 
D)  $f ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 28 x - 34$

Question 5

Find the axis of the graph of the function.
-$$f ( x ) = ( x + 2 ) ^ { 2 } + 6$$

Accepted Answer

A)  $x = 0$ 
B)  $x = - 2$ 
C)  $y = - 2$ 
D)  $x = 2$ 
A)  $x = 0$ 
B)  $x = - 2$ 
C)  $y = - 2$ 
D)  $x = 2$

Question 6

Write the statement as a power function equation. Use k as the constant of variation.
-The height $h$ of a triangle with a fixed area varies inversely as the base $b$.

Accepted Answer

A)  $b = k h$ 
B)  $h = \mathrm { kb }$ 
C)  $h = \frac { k } { b }$ 
D)  $h = \frac { b } { k }$ 
A)  $b = k h$ 
B)  $h = \mathrm { kb }$ 
C)  $h = \frac { k } { b }$ 
D)  $h = \frac { b } { k }$

Question 7

Describe the strength and direction of the linear correlation.
-

Accepted Answer

A)  Weak negative linear correlation 
B)  Strong negative linear correlation 
C)  Little or no linear correlation 
D)  Strong positive linear correlation 
A)  Weak negative linear correlation 
B)  Strong negative linear correlation 
C)  Little or no linear correlation 
D)  Strong positive linear correlation

Question 8

Match the given graph with its polynomial function.Choose the one alternative that best completes the statement or answers the question.
-

Accepted Answer

A)  $f ( x ) = x ^ { 4 } - 5 x ^ { 3 } + 6 x ^ { 2 } + x + 10$ 
B)  $f ( x ) = - x ^ { 3 } + 15 x ^ { 2 } + x - 10$ 
C)  $f ( x ) = x ^ { 5 } + 3 x ^ { 4 } - 5 x ^ { 3 } - 15 x ^ { 2 } + x + 10$ 
D)  $f ( x ) = - x ^ { 5 } - 5 x ^ { 3 } - 6 x ^ { 2 } + 10 x$ 
A)  $f ( x ) = x ^ { 4 } - 5 x ^ { 3 } + 6 x ^ { 2 } + x + 10$ 
B)  $f ( x ) = - x ^ { 3 } + 15 x ^ { 2 } + x - 10$ 
C)  $f ( x ) = x ^ { 5 } + 3 x ^ { 4 } - 5 x ^ { 3 } - 15 x ^ { 2 } + x + 10$ 
D)  $f ( x ) = - x ^ { 5 } - 5 x ^ { 3 } - 6 x ^ { 2 } + 10 x$

Question 9

Use synthetic division to determine whether the number k is an upper or lower bound (as specified) for the real zeros of
the function f.
-$k = 2 ; f ( x ) = 2 x ^ { 3 } + 3 x ^ { 2 } + 5 x - 5$; Lower bound?

Accepted Answer

A) True 
 B)False

Question 10

State how many complex and real zeros the function has.
-$$f ( x ) = x ^ { 4 } - 48 x ^ { 2 } - 49$$

Accepted Answer

A)  4 complex zeros; none real 
B)  4 complex zeros; 2 real 
C)  4 complex zeros; all 4 real 
D)  4 complex zeros; 1 real 
A)  4 complex zeros; none real 
B)  4 complex zeros; 2 real 
C)  4 complex zeros; all 4 real 
D)  4 complex zeros; 1 real

Question 11

Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial.
-$$x - 5 ; 3 x ^ { 2 } - 4 x + 95$$

Accepted Answer

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

Question 12

Use the Rational Zeros Theorem to write a list of all potential rational zeros
-$$f ( x ) = 2 x ^ { 3 } + 8 x ^ { 2 } + 12 x - 8$$

Accepted Answer

A)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 4 } , \pm \frac { 1 } { 8 } , \pm 2$ 
B)  $\pm 1 , \pm 2 , \pm 4$ 
C)  $\pm 1 , \pm 2 , \pm 4 , \pm 8$ 
D)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 2 , \pm 4 , \pm 8$ 
A)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 4 } , \pm \frac { 1 } { 8 } , \pm 2$ 
B)  $\pm 1 , \pm 2 , \pm 4$ 
C)  $\pm 1 , \pm 2 , \pm 4 , \pm 8$ 
D)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 2 , \pm 4 , \pm 8$

Question 13

Write the function as a product of linear and irreducible quadratic factors, all with real coefficients.
-$$f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 12 x ^ { 2 } - 24 x + 32$$

Accepted Answer

A)  $( x - 4 ) ( x - 2 ) \left( x ^ { 2 } + 1 \right)$ 
B)  $( x - 4 ) ( x - 2 ) \left( x ^ { 2 } + 4 \right)$ 
C)  $( x - 4 ) ( x + 2 ) \left( x ^ { 2 } + 4 \right)$ 
D)  $( x + 4 ) ( x - 2 ) \left( x ^ { 2 } + 4 \right)$ 
A)  $( x - 4 ) ( x - 2 ) \left( x ^ { 2 } + 1 \right)$ 
B)  $( x - 4 ) ( x - 2 ) \left( x ^ { 2 } + 4 \right)$ 
C)  $( x - 4 ) ( x + 2 ) \left( x ^ { 2 } + 4 \right)$ 
D)  $( x + 4 ) ( x - 2 ) \left( x ^ { 2 } + 4 \right)$

Question 14

Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or irrational.
-$$f ( x ) = x ^ { 4 } + 9 x ^ { 3 } + 7 x ^ { 2 } - 117 x - 260$$

Accepted Answer

A)  $- 5$ (rational), $- 4$ (rational), $\sqrt { 13 }$ (irrational), and $- \sqrt { 13 }$ (irrational) 
B)  5 (rational), 4 (rational), $2 + \sqrt { 13 }$ (irrational), and $2 - \sqrt { 13 }$ (irrational) 
C)  5 (rational), 4 (rational), $\sqrt { 13 }$ (irrational), and $- \sqrt { 13 }$ (irrational) 
D)  $- 5$ (rational), $- 4$ (rational), $2 + \sqrt { 13 }$ (irrational), and $2 - \sqrt { 13 }$ (irrational) 
A)  $- 5$ (rational), $- 4$ (rational), $\sqrt { 13 }$ (irrational), and $- \sqrt { 13 }$ (irrational) 
B)  5 (rational), 4 (rational), $2 + \sqrt { 13 }$ (irrational), and $2 - \sqrt { 13 }$ (irrational) 
C)  5 (rational), 4 (rational), $\sqrt { 13 }$ (irrational), and $- \sqrt { 13 }$ (irrational) 
D)  $- 5$ (rational), $- 4$ (rational), $2 + \sqrt { 13 }$ (irrational), and $2 - \sqrt { 13 }$ (irrational)

Question 15

Solve the problem. Round as appropriate.
-The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 2.25 lb when the masses are 4 ft apart, what is the attraction when the masses are 6 ft
Apart?

Accepted Answer

A)  1 lb 
B)  4 lb 
C)  2 lb 
D)  3 lb 
A)  1 lb 
B)  4 lb 
C)  2 lb 
D)  3 lb

Question 16

Find the vertex of the graph of the function.
-$$f ( x ) = 4 ( x - 3 ) ^ { 2 } + 4$$

Accepted Answer

A)  $( - 3,4 )$ 
B)  $( 3 , - 4 )$ 
C)  $( 3,4 )$ 
D)  $( - 3 , - 4 )$ 
A)  $( - 3,4 )$ 
B)  $( 3 , - 4 )$ 
C)  $( 3,4 )$ 
D)  $( - 3 , - 4 )$

Question 17

Determine if the function is a power function. If it is, then state the power and constant of variation.
-$$\mathrm { C } = 2 \pi \mathrm { r }$$

Accepted Answer

A)  Not a power function 
B)  Power is 1; constant of variation is $2 \pi$ 
C)  Power is 0 ; constant of variation is $2 \pi$ 
D)  Power is 2; constant of variation is $\pi$ 
A)  Not a power function 
B)  Power is 1; constant of variation is $2 \pi$ 
C)  Power is 0 ; constant of variation is $2 \pi$ 
D)  Power is 2; constant of variation is $\pi$

Question 18

Solve the inequality.
-$$\frac { x ^ { 2 } ( x - 4 ) } { ( x + 3 ) ^ { 3 } } < 0$$

Accepted Answer

A)  $( - 3,0 ) \cup ( 4 , \infty )$ 
B)  $( - 3,0 ) \cup ( 0,4 )$ 
C)  $( - 3,4 )$ 
D)  $( - \infty , - 3 ) \cup ( 0,4 )$ 
A)  $( - 3,0 ) \cup ( 4 , \infty )$ 
B)  $( - 3,0 ) \cup ( 0,4 )$ 
C)  $( - 3,4 )$ 
D)  $( - \infty , - 3 ) \cup ( 0,4 )$

Question 19

If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact.
-$$f ( x ) = 16 x ^ { 5 } + 6 x ^ { 4 } - 9 x ^ { 3 }$$

Accepted Answer

A)  Degree: 5; leading coefficient: 16 
B)  Degree: 16; leading coefficient: 5 
C)  Not a polynomial function. 
D)  Degree: 3 ; leading coefficient: 16 
A)  Degree: 5; leading coefficient: 16 
B)  Degree: 16; leading coefficient: 5 
C)  Not a polynomial function. 
D)  Degree: 3 ; leading coefficient: 16

Question 20

Match the polynomial function graph to the appropriate zeros and multiplicities.
-

Accepted Answer

A)  4 (multiplicity 4), 1 (multiplicity 4) 
B)  1 (multiplicity 3), 4 (multiplicity 2) 
C)  4 (multiplicity 4), 1 (multiplicity 3 ) 
D)  1 (multiplicity 4), 4 (multiplicity 3 ) 
A)  4 (multiplicity 4), 1 (multiplicity 4) 
B)  1 (multiplicity 3), 4 (multiplicity 2) 
C)  4 (multiplicity 4), 1 (multiplicity 3 ) 
D)  1 (multiplicity 4), 4 (multiplicity 3 )

Find the requested function. -Find the polynomial function with leading coefficient 6 ; degree 3 ; and $- 3,4$ , and $- 4$ as zeros.

Find the zeros of the function. - $f ( x ) = x ^ { 3 } + 12 x ^ { 2 } + 41 x + 42$

Find the vertex of the graph of the function. - $f ( x ) = 6 x ^ { 2 } - 84 x + 304$

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. - $- 1$ and $3 + 5 \mathrm { i }$

Find the axis of the graph of the function. - $f ( x ) = ( x + 2 ) ^ { 2 } + 6$

Write the statement as a power function equation. Use k as the constant of variation. -The height $h$ of a triangle with a fixed area varies inversely as the base $b$ .

Describe the strength and direction of the linear correlation. -

Match the given graph with its polynomial function.Choose the one alternative that best completes the statement or answers the question. -

Use synthetic division to determine whether the number k is an upper or lower bound (as specified) for the real zeros of the function f. - $k = 2 ; f ( x ) = 2 x ^ { 3 } + 3 x ^ { 2 } + 5 x - 5$ ; Lower bound?

State how many complex and real zeros the function has. - $f ( x ) = x ^ { 4 } - 48 x ^ { 2 } - 49$

Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial. - $x - 5 ; 3 x ^ { 2 } - 4 x + 95$

Use the Rational Zeros Theorem to write a list of all potential rational zeros - $f ( x ) = 2 x ^ { 3 } + 8 x ^ { 2 } + 12 x - 8$

Write the function as a product of linear and irreducible quadratic factors, all with real coefficients. - $f ( x ) = x ^ { 4 } - 6 x ^ { 3 } + 12 x ^ { 2 } - 24 x + 32$

Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or irrational. - $f ( x ) = x ^ { 4 } + 9 x ^ { 3 } + 7 x ^ { 2 } - 117 x - 260$

Solve the problem. Round as appropriate. -The gravitational attraction A between two masses varies inversely as the square of the distance between them. The force of attraction is 2.25 lb when the masses are 4 ft apart, what is the attraction when the masses are 6 ft Apart?

Find the vertex of the graph of the function. - $f ( x ) = 4 ( x - 3 ) ^ { 2 } + 4$

Determine if the function is a power function. If it is, then state the power and constant of variation. - $\mathrm { C } = 2 \pi \mathrm { r }$

Solve the inequality. - $\frac { x ^ { 2 } ( x - 4 ) } { ( x + 3 ) ^ { 3 } } < 0$

If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact. - $f ( x ) = 16 x ^ { 5 } + 6 x ^ { 4 } - 9 x ^ { 3 }$

Match the polynomial function graph to the appropriate zeros and multiplicities. -

Functions and Graphs

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Exam 2: Polynomial, Power, and Rational Functions

Find the requested function. -Find the polynomial function with leading coefficient 6 ; degree 3 ; and −3,4- 3,4−3,4 , and −4- 4−4 as zeros.

Find the zeros of the function. - f(x)=x3+12x2+41x+42f ( x ) = x ^ { 3 } + 12 x ^ { 2 } + 41 x + 42f(x)=x3+12x2+41x+42

Find the vertex of the graph of the function. - f(x)=6x2−84x+304f ( x ) = 6 x ^ { 2 } - 84 x + 304f(x)=6x2−84x+304

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. - −1- 1−1 and 3+5i3 + 5 \mathrm { i }3+5i

Find the axis of the graph of the function. - f(x)=(x+2)2+6f ( x ) = ( x + 2 ) ^ { 2 } + 6f(x)=(x+2)2+6

Write the statement as a power function equation. Use k as the constant of variation. -The height hhh of a triangle with a fixed area varies inversely as the base bbb .