Question 1

Determine if the function is a power function. If it is, then state the power and constant of variation.
-$$f ( x ) = 0 \cdot x ^ { 3 }$$

Accepted Answer

A)  Power is 3; constant of variation is 0 
B)  Not a power function 
C)  Power is 3; constant of variation is 1 
D)  Power is 0; constant of variation is 3 
A)  Power is 3; constant of variation is 0 
B)  Not a power function 
C)  Power is 3; constant of variation is 1 
D)  Power is 0; constant of variation is 3

Question 2

Find all rational zeros.
-$$f ( x ) = x ^ { 4 } + 2 x ^ { 3 } + 2 x ^ { 2 } - 4 x - 8$$

Accepted Answer

A)  $- 2 , - 3$ 
B)  $2 , - 1$ 
C)  $- 2,2$ 
D)  No rational zeros 
A)  $- 2 , - 3$ 
B)  $2 , - 1$ 
C)  $- 2,2$ 
D)  No rational zeros

Question 3

Solve the polynomial inequality.
-$$x ^ { 4 } - 145 x ^ { 2 } + 5184 < 0$$

Accepted Answer

A)  $( - 9,9 )$ 
B)  $( - \infty , - 8 ) \cup ( 8 , \infty )$ 
C)  $( - 9 , - 8 ) \cup ( 8,9 )$ 
D)  $( - 9 , - 8 ) \cap ( 8,9 )$ 
A)  $( - 9,9 )$ 
B)  $( - \infty , - 8 ) \cup ( 8 , \infty )$ 
C)  $( - 9 , - 8 ) \cup ( 8,9 )$ 
D)  $( - 9 , - 8 ) \cap ( 8,9 )$

Question 4

Using the given zero, find all other zeros of f(x).
-$i$ is a zero of $f ( x ) = x ^ { 4 } - 8 x ^ { 3 } + 14 x ^ { 2 } - 8 x + 13$

Accepted Answer

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

Question 5

Describe the strength and direction of the linear correlation.
-Several people of various weights were given IQ tests. Their weights and IQs are recorded in the following table:

Accepted Answer

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

Question 6

Use a cubic or quartic regression (as specified) to fit a curve through the points given in the table. Round to the nearest
hundredth.
-

Accepted Answer

A)  $y \approx - 1.53 x ^ { 3 } + 0.24 x ^ { 2 } - 2.07 x + 0.36$ 
B)  $y \approx - 1.53 x ^ { 3 } + 0.54 x ^ { 2 } - 2.07 x + 0.36$ 
C)  $y \approx - 1.83 x ^ { 3 } + 0.24 x ^ { 2 } - 2.07 x + 0.36$ 
D)  $y \approx - 1.53 x ^ { 3 } + 0.24 x ^ { 2 } - 2.57 x + 0.36$ 
A)  $y \approx - 1.53 x ^ { 3 } + 0.24 x ^ { 2 } - 2.07 x + 0.36$ 
B)  $y \approx - 1.53 x ^ { 3 } + 0.54 x ^ { 2 } - 2.07 x + 0.36$ 
C)  $y \approx - 1.83 x ^ { 3 } + 0.24 x ^ { 2 } - 2.07 x + 0.36$ 
D)  $y \approx - 1.53 x ^ { 3 } + 0.24 x ^ { 2 } - 2.57 x + 0.36$

Question 7

Choose the one alternative that best completes the statement or answers the question.
Solve the equation.
-$$\frac { 12 } { x - 4 } = 1 + \frac { 14 } { x + 4 }$$

Accepted Answer

A)  $x = - 14$ or 12 
B)  $x = 10$ or $- 12$ 
C)  $x = - 10$ or 12 
D)  $\varnothing$ 
A)  $x = - 14$ or 12 
B)  $x = 10$ or $- 12$ 
C)  $x = - 10$ or 12 
D)  $\varnothing$

Question 8

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

Accepted Answer

A)  $- 2$ (multiplicity 4), 3 (multiplicity 3 ) 
B)  $- 2$ (multiplicity 3 ), 3 (multiplicity 4 ) 
C)  $- 2$ (multiplicity 4), 3 (multiplicity 4) 
D)  $- 2$ (multiplicity 3), 3 (multiplicity 2) 
A)  $- 2$ (multiplicity 4), 3 (multiplicity 3 ) 
B)  $- 2$ (multiplicity 3 ), 3 (multiplicity 4 ) 
C)  $- 2$ (multiplicity 4), 3 (multiplicity 4) 
D)  $- 2$ (multiplicity 3), 3 (multiplicity 2)

Question 9

Graph the function in a viewing window that shows all of its extrema and x-intercepts.
-$$f ( x ) = ( x + 1 ) ^ { 3 } ( x + 2 ) ( x - 1 )$$

Accepted Answer

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

Question 10

Solve the problem.
-The polynomial function $L ( p ) = p ^ { 3 } - 5 p ^ { 2 } + 20$ gives the rate of gas leakage from a tank as pressure increases in $p$ units from its initial setting. Will an increase of 4 units result in a lower rate of leakage compared to the initial setting?

Accepted Answer

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

Question 11

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.
-$k = 4 ; f ( x ) = 5 x ^ { 3 } - 2 x ^ { 2 } - 4 x + 2 ;$ Upper bound?

Accepted Answer

A) True 
 B)False

Question 12

Describe the strength and direction of the linear correlation.
-Several people of various ages were timed running an obstacle course. Their ages and times are recorded in the following table:

Accepted Answer

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

Question 13

Find the requested function.
-Find the polynomial function with leading coefficient -6; degree 4 ; and $1,4,6$, and $- 6$ as zeros.

Accepted Answer

A)  $f ( x ) = ( x - 1 ) ( x - 4 ) ( x - 6 ) ( x + 6 )$ 
B)  $f ( x ) = - 6 x ( x - 1 ) ( x - 4 ) ( x - 6 ) ( x + 6 )$ 
C)  $f ( x ) = - 6 ( x + 1 ) ( x + 4 ) ( x + 6 ) ( x - 6 )$ 
D)  $f ( x ) = - 6 ( x - 1 ) ( x - 4 ) ( x - 6 ) ( x + 6 )$ 
A)  $f ( x ) = ( x - 1 ) ( x - 4 ) ( x - 6 ) ( x + 6 )$ 
B)  $f ( x ) = - 6 x ( x - 1 ) ( x - 4 ) ( x - 6 ) ( x + 6 )$ 
C)  $f ( x ) = - 6 ( x + 1 ) ( x + 4 ) ( x + 6 ) ( x - 6 )$ 
D)  $f ( x ) = - 6 ( x - 1 ) ( x - 4 ) ( x - 6 ) ( x + 6 )$

Question 14

Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial.
-$$x + 5 ; 3 x ^ { 3 } + 12 x ^ { 2 } - 14 x + 5$$

Accepted Answer

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

Question 15

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

Accepted Answer

A)  $- 2 , - 5 , - 5$ 
B)  $- 2,5 , - 5$ 
C)  $- \frac { 1 } { 10 } , 1 , - 5$ 
D)  $- \frac { 1 } { 2 } , \frac { 1 } { 5 } , - 5$ 
A)  $- 2 , - 5 , - 5$ 
B)  $- 2,5 , - 5$ 
C)  $- \frac { 1 } { 10 } , 1 , - 5$ 
D)  $- \frac { 1 } { 2 } , \frac { 1 } { 5 } , - 5$

Question 16

Solve the problem.
-Bill Monotone sells used CDs for $\$ 9.25$ each. Each used CD costs him $\$ 3.75$. His overhead is $\$ 6700$. Express the cost $C$ as a function of $x$ where $x$ is the number of CDs sold.

Accepted Answer

A)  $C ( x ) = 9.25 x + 6700$ 
B)  $C ( x ) = 6700 x + 3.75$ 
C)  $C ( x ) = 6700 x + 9.25$ 
D)  $C ( x ) = 3.75 x + 6700$ 
A)  $C ( x ) = 9.25 x + 6700$ 
B)  $C ( x ) = 6700 x + 3.75$ 
C)  $C ( x ) = 6700 x + 9.25$ 
D)  $C ( x ) = 3.75 x + 6700$

Question 17

State how many complex and real zeros the function has.
-$$f ( x ) = x ^ { 3 } - 15 x ^ { 2 } + 75 x - 125$$

Accepted Answer

A)  3 complex zeros; 1 real 
B)  3 complex zeros; none real 
C)  3 complex zeros; all 3 real 
D)  3 complex zeros; 2 real 
A)  3 complex zeros; 1 real 
B)  3 complex zeros; none real 
C)  3 complex zeros; all 3 real 
D)  3 complex zeros; 2 real

Question 18

Divide using synthetic division, and write a summary statement in fraction form.
-$$\frac { - 6 x ^ { 3 } + 2 x ^ { 2 } + 5 x - 10 } { x - 2 }$$

Accepted Answer

A)  $- 6 x ^ { 2 } - 10 x - 15 + \frac { - 40 } { x + 2 }$ 
B)  $- 6 x ^ { 2 } - 10 x + 15 + \frac { - 40 } { x + 2 }$ 
C)  $- 6 x ^ { 2 } + 10 x + 25 + \frac { - 40 } { x + 2 }$ 
D)  $- 6 x ^ { 2 } + 10 x - 25 + \frac { - 40 } { x + 2 }$ 
A)  $- 6 x ^ { 2 } - 10 x - 15 + \frac { - 40 } { x + 2 }$ 
B)  $- 6 x ^ { 2 } - 10 x + 15 + \frac { - 40 } { x + 2 }$ 
C)  $- 6 x ^ { 2 } + 10 x + 25 + \frac { - 40 } { x + 2 }$ 
D)  $- 6 x ^ { 2 } + 10 x - 25 + \frac { - 40 } { x + 2 }$

Question 19

State how many complex and real zeros the function has.
-$$f ( x ) = x ^ { 5 } + 7 x ^ { 4 } + 2 x ^ { 3 } + 14 x ^ { 2 } + x + 7$$

Accepted Answer

A)  5 complex zeros; 1 real 
B)  5 complex zeros; all 5 real 
C)  5 complex zeros; 3 real 
D)  5 complex zeros; 2 real 
A)  5 complex zeros; 1 real 
B)  5 complex zeros; all 5 real 
C)  5 complex zeros; 3 real 
D)  5 complex zeros; 2 real

Question 20

For the given function, find all asymptotes of the type indicated (if there are any)
-$f ( x ) = \frac { x ^ { 2 } - 4 x + 3 } { x + 6 }$, slant

Accepted Answer

A)  $y = x - 10$ 
B)  $x = y + 4$ 
C)  $y = x + 7$ 
D)  None 
A)  $y = x - 10$ 
B)  $x = y + 4$ 
C)  $y = x + 7$ 
D)  None

Determine if the function is a power function. If it is, then state the power and constant of variation. - $f ( x ) = 0 \cdot x ^ { 3 }$

Find all rational zeros. - $f ( x ) = x ^ { 4 } + 2 x ^ { 3 } + 2 x ^ { 2 } - 4 x - 8$

Solve the polynomial inequality. - $x ^ { 4 } - 145 x ^ { 2 } + 5184 < 0$

Using the given zero, find all other zeros of f(x). - $i$ is a zero of $f ( x ) = x ^ { 4 } - 8 x ^ { 3 } + 14 x ^ { 2 } - 8 x + 13$

Describe the strength and direction of the linear correlation. -Several people of various weights were given IQ tests. Their weights and IQs are recorded in the following table:

Use a cubic or quartic regression (as specified) to fit a curve through the points given in the table. Round to the nearest hundredth. -

Choose the one alternative that best completes the statement or answers the question. Solve the equation. - $\frac { 12 } { x - 4 } = 1 + \frac { 14 } { x + 4 }$

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

Graph the function in a viewing window that shows all of its extrema and x-intercepts. - $f ( x ) = ( x + 1 ) ^ { 3 } ( x + 2 ) ( x - 1 )$ $Graph the function in a viewing window that shows all of its extrema and x-intercepts. - f ( x ) = ( x + 1 ) ^ { 3 } ( x + 2 ) ( x - 1 )$

Solve the problem. -The polynomial function $L ( p ) = p ^ { 3 } - 5 p ^ { 2 } + 20$ gives the rate of gas leakage from a tank as pressure increases in $p$ units from its initial setting. Will an increase of 4 units result in a lower rate of leakage compared to the initial setting?

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. - $k = 4 ; f ( x ) = 5 x ^ { 3 } - 2 x ^ { 2 } - 4 x + 2 ;$ Upper bound?

Describe the strength and direction of the linear correlation. -Several people of various ages were timed running an obstacle course. Their ages and times are recorded in the following table:

Find the requested function. -Find the polynomial function with leading coefficient -6; degree 4 ; and $1,4,6$ , and $- 6$ as zeros.

Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial. - $x + 5 ; 3 x ^ { 3 } + 12 x ^ { 2 } - 14 x + 5$

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

Solve the problem. -Bill Monotone sells used CDs for $\$ 9.25$ each. Each used CD costs him $\$ 3.75$ . His overhead is $\$ 6700$ . Express the cost $C$ as a function of $x$ where $x$ is the number of CDs sold.

State how many complex and real zeros the function has. - $f ( x ) = x ^ { 3 } - 15 x ^ { 2 } + 75 x - 125$

Divide using synthetic division, and write a summary statement in fraction form. - $\frac { - 6 x ^ { 3 } + 2 x ^ { 2 } + 5 x - 10 } { x - 2 }$

State how many complex and real zeros the function has. - $f ( x ) = x ^ { 5 } + 7 x ^ { 4 } + 2 x ^ { 3 } + 14 x ^ { 2 } + x + 7$

For the given function, find all asymptotes of the type indicated (if there are any) - $f ( x ) = \frac { x ^ { 2 } - 4 x + 3 } { x + 6 }$ , slant

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Exam 2: Polynomial, Power, and Rational Functions

Determine if the function is a power function. If it is, then state the power and constant of variation. - f(x)=0⋅x3f ( x ) = 0 \cdot x ^ { 3 }f(x)=0⋅x3

Find all rational zeros. - f(x)=x4+2x3+2x2−4x−8f ( x ) = x ^ { 4 } + 2 x ^ { 3 } + 2 x ^ { 2 } - 4 x - 8f(x)=x4+2x3+2x2−4x−8

Solve the polynomial inequality. - x4−145x2+5184<0x ^ { 4 } - 145 x ^ { 2 } + 5184 < 0x4−145x2+5184<0

Using the given zero, find all other zeros of f(x). - iii is a zero of f(x)=x4−8x3+14x2−8x+13f ( x ) = x ^ { 4 } - 8 x ^ { 3 } + 14 x ^ { 2 } - 8 x + 13f(x)=x4−8x3+14x2−8x+13