Question 1

Determine whether the polynomial function is cubic or quartic.
-

Accepted Answer

A)  Cubic 
B)  Quartic 
A)  Cubic 
B)  Quartic

Question 2

Use synthetic division to find the quotient and remainder.
-$$\left( 2 x ^ { 3 } + 3 x ^ { 2 } + 4 x - 10 \right) \div ( x + 1 )$$

Accepted Answer

A)  $2 x ^ { 2 } + 5 x + 9 + \frac { 1 } { x + 1 }$ 
B)  $2 x ^ { 2 } + x + 3 + \frac { 13 } { x + 1 }$ 
C)  $2 x ^ { 2 } + x + 3 - \frac { 13 } { x + 1 }$ 
D)  $2 x ^ { 2 } + 5 x + 9 - \frac { 1 } { x + 1 }$ 
A)  $2 x ^ { 2 } + 5 x + 9 + \frac { 1 } { x + 1 }$ 
B)  $2 x ^ { 2 } + x + 3 + \frac { 13 } { x + 1 }$ 
C)  $2 x ^ { 2 } + x + 3 - \frac { 13 } { x + 1 }$ 
D)  $2 x ^ { 2 } + 5 x + 9 - \frac { 1 } { x + 1 }$

Question 3

$2 x ^ { 3 } + 9 x ^ { 2 } - 27 x - 54 > 0$

Accepted Answer

A)  $x \leq - 6 \text { or } - \frac { 3 } { 2 } \leq x \leq 3$ 
B)  $x  3$ 
A)  $x \leq - 6 \text { or } - \frac { 3 } { 2 } \leq x \leq 3$ 
B)  $x  3$

Question 4

Use a graphing calculator to estimate the local maximum and local minimum values of the function to the nearest
hundredth.
-The polynomial $G ( x ) = - 0.006 x ^ { 4 } + 0.140 x ^ { 3 } - 0.53 x ^ { 2 } + 1.79 x$ measures the concentration of a dye in the bloodstream x seconds after it is injected. Does the concentration increase between 12 and 13 seconds?

Accepted Answer

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

Question 5

Use algebraic and/or graphical methods to solve the inequality.
-$$( x + 1 ) ( x - 3 ) ( x - 8 ) > 0$$

Accepted Answer

A)  $x  8$ 
C)  $- 1  8$ 
D)  $x < 3$ 
A)  $x  8$ 
C)  $- 1  8$ 
D)  $x < 3$

Question 6

At a ticket booth, customers arrive randomly at a rate of  x  per hour. The average line length is  $f ( x ) = \frac { x ^ { 2 } } { 400 - 20 x }$  where $0 \leq x < 20$ To keep the time waiting in line reasonable, it is decided that the average line length should not exceed 6 customers. Solve the inequality $\frac { x ^ { 2 } } { 400 - 20 x } \leq 6$ to determine the rates  x  per hour at which customers can arrive before a second attendant is needed.

Accepted Answer

A)  $0 \leq x \leq 17$ 
B)  $0 \leq x \leq 18$ 
C)  $0 \leq x \leq 16$ 
D)  $0 \leq x \leq 19$ 
A)  $0 \leq x \leq 17$ 
B)  $0 \leq x \leq 18$ 
C)  $0 \leq x \leq 16$ 
D)  $0 \leq x \leq 19$

Question 7

Provide an appropriate response.
-If Q varies inversely as the square roo $R \text { and } Q = 2 \text { when } R = 9$ , what is Q when R is 16?

Accepted Answer

A)  1.5 
B)  2.66666667 
C)  4.5 
D)  24 
A)  1.5 
B)  2.66666667 
C)  4.5 
D)  24

Question 8

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions.
-$7 x ^ { 4 } + 9 x ^ { 3 } - 26 x ^ { 2 } - 36 x - 8 = 0 ; - 1$

Accepted Answer

A)  $- \frac { 2 } { 7 } , - 2 , - 2$ 
B)  $\frac { 2 } { 7 } , 2,2$ 
C)  $- \frac { 2 } { 7 } , 2 , - 2$ 
D)  $\frac { 2 } { 7 } , 2 , - 2$ 
A)  $- \frac { 2 } { 7 } , - 2 , - 2$ 
B)  $\frac { 2 } { 7 } , 2,2$ 
C)  $- \frac { 2 } { 7 } , 2 , - 2$ 
D)  $\frac { 2 } { 7 } , 2 , - 2$

Question 9

Use the graph of f(x) to solve the inequality.
-$f(x)<0$

Accepted Answer

A)  $- 6  4$ 
B)  $x < - 1$ or $4 < x < 6$ 
C)  $x < - 6$ or $- 1 < x < 4$ 
D)  $x < 6$ or $1 < x < 4$ 
A)  $- 6  4$ 
B)  $x < - 1$ or $4 < x < 6$ 
C)  $x < - 6$ or $- 1 < x < 4$ 
D)  $x < 6$ or $1 < x < 4$

Question 10

Use algebraic and/or graphical methods to solve the inequality.
-$$( x + 7 ) ( x + 6 ) ( x - 5 ) < 0$$

Accepted Answer

A) $x 5$ C) $x > 5$ D) $x < - 7$ or $- 6 < x < 5$ A) $x 5$ C) $x > 5$ D) $x < - 7$ or $- 6 < x < 5$

Question 11

Give the equations of any vertical asymptotes for the graphs of the rational functions.
-$$f ( x ) = \frac { 5 x + 2 } { 5 x - 3 }$$

Accepted Answer

A)  $x = \frac { 3 } { 5 }$ 
B)  $x = 1$ 
C)  $x = - \frac { 5 } { 3 }$ 
D)  $x = \frac { 5 } { 3 }$ 
A)  $x = \frac { 3 } { 5 }$ 
B)  $x = 1$ 
C)  $x = - \frac { 5 } { 3 }$ 
D)  $x = \frac { 5 } { 3 }$

Question 12

The future value of $7000 invested for 5 years at rate r, compounded annually, is given by $S = 7000 ( 1 + r ) ^ { 5 }$ Find the rate r, as a percent, that gives a future value of $9817.86. Round to the nearest whole percent.

Accepted Answer

A)  10% 
B)  8% 
C)  6% 
D)  7% 
A)  10% 
B)  8% 
C)  6% 
D)  7%

Question 13

Determine all possible rational solutions of the polynomial equation.
-$$f ( x ) = x ^ { 3 } - 6 x ^ { 2 } + 4 x - 24$$

Accepted Answer

A)  $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 8 , \pm 12 , \pm 24$ 
B)  $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 12 , \pm 24$ 
C)  $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 24$ 
D)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 8 , \pm 12 , \pm 24$ 
A)  $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 8 , \pm 12 , \pm 24$ 
B)  $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 12 , \pm 24$ 
C)  $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 24$ 
D)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 8 , \pm 12 , \pm 24$

Question 14

An open-top box is to be made by cutting small identical squares from each corner of a 12 -by-12-in. sheet of tin and bending up the sides. If each corner square is  x  inches on a side, the volume of the box (in in.  3) is given by $V ( x ) = 144 x - 48 x ^ { 2 } + 4 x ^ { 3 }$. By sketching the graph of  V(x) , estimate what values of  x  result in a box with a volume greater than 64 in3 .

Accepted Answer

A)  $1.0 \text { in. } \leq x \leq 3.0 \text { in }$ 
B)  $0.1 \text { in. } \leq x \leq 5.0 \text { in }$ 
C)  $0.54 \text { in. } \leq x \leq 4 \text { in. }$ 
D)  $1.5 \text { in. } \leq x \leq 2.5 \text { in. }$ 
A)  $1.0 \text { in. } \leq x \leq 3.0 \text { in }$ 
B)  $0.1 \text { in. } \leq x \leq 5.0 \text { in }$ 
C)  $0.54 \text { in. } \leq x \leq 4 \text { in. }$ 
D)  $1.5 \text { in. } \leq x \leq 2.5 \text { in. }$

Question 15

Solve the polynomial equation.
-$$( 2 x + 9 ) ^ { 2 } ( 8 - x ) ^ { 2 } = 0$$

Accepted Answer

A)  $- \frac { 9 } { 2 } , \frac { 9 } { 2 } , - 8,8$ 
B)  $- 9,8$ 
C)  $- \frac { 9 } { 2 } , 8$ 
D)  $\frac { 9 } { 2 } , - 8$ 
A)  $- \frac { 9 } { 2 } , \frac { 9 } { 2 } , - 8,8$ 
B)  $- 9,8$ 
C)  $- \frac { 9 } { 2 } , 8$ 
D)  $\frac { 9 } { 2 } , - 8$

Question 16

Graph the function.
-$$f ( x ) = \frac { x ^ { 2 } - x - 12 } { x + 4 }$$

Accepted Answer

A)   
B)   2 
C)   
D)   
A)   
B)   2 
C)   
D)

Question 17

Match the polynomial function with the graph.
-$$y = x ^ { 4 } - 0.5 x ^ { 3 } - 15.5 x ^ { 2 } + 17 x + 14$$

Accepted Answer

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

Question 18

$f ( x ) = 0.62 x ^ { 3 } - 5 x ^ { 2 } + 11 x + 8$

Accepted Answer

A)   [-10,5]  by  [-300,300] 
B)   [-30,80]  by  [-8000,4000] 
C)   [-10,10]  by  [-10,10] 
D)   [-5,10]  by  [-100,300] 
A)   [-10,5]  by  [-300,300] 
B)   [-30,80]  by  [-8000,4000] 
C)   [-10,10]  by  [-10,10] 
D)   [-5,10]  by  [-100,300]

Question 19

Suppose a cost-benefit model is given b $y = \frac { 7.7 x } { 100 - x }$ where y is the cost in thousands of dollars for removing x percent of a given pollutant. Find the cost of removing 45% to the nearest dollar.

Accepted Answer

A)  $6300 
B)  $3465 
C)  $7700 
D)  $818 
A)  $6300 
B)  $3465 
C)  $7700 
D)  $818

Question 20

Use graphical methods to find any turning points of the graph of the function.
-$$f ( x ) = \frac { x ^ { 2 } - 8 x + 16 } { x - 5 }$$

Accepted Answer

A)  No turning points 
B)  $( 0,16 ) , ( 4,0 )$, and $( 14,11.11 )$ 
C)  $( 4,0 )$ and $( 6,4 )$ 
D)  $( 14,4 )$ and $( 4,0 )$ 
A)  No turning points 
B)  $( 0,16 ) , ( 4,0 )$, and $( 14,11.11 )$ 
C)  $( 4,0 )$ and $( 6,4 )$ 
D)  $( 14,4 )$ and $( 4,0 )$

Determine whether the polynomial function is cubic or quartic. -

Use synthetic division to find the quotient and remainder. - $\left( 2 x ^ { 3 } + 3 x ^ { 2 } + 4 x - 10 \right) \div ( x + 1 )$

$2 x ^ { 3 } + 9 x ^ { 2 } - 27 x - 54 > 0$

Use algebraic and/or graphical methods to solve the inequality. - $( x + 1 ) ( x - 3 ) ( x - 8 ) > 0$

Provide an appropriate response. -If Q varies inversely as the square roo $R \text { and } Q = 2 \text { when } R = 9$ , what is Q when R is 16?

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions. - $7 x ^ { 4 } + 9 x ^ { 3 } - 26 x ^ { 2 } - 36 x - 8 = 0 ; - 1$

Use the graph of f(x) to solve the inequality. - $f(x)<0$

Use algebraic and/or graphical methods to solve the inequality. - $( x + 7 ) ( x + 6 ) ( x - 5 ) < 0$

Give the equations of any vertical asymptotes for the graphs of the rational functions. - $f ( x ) = \frac { 5 x + 2 } { 5 x - 3 }$

The future value of $7000 invested for 5 years at rate r, compounded annually, is given by $S = 7000 ( 1 + r ) ^ { 5 }$ Find the rate r, as a percent, that gives a future value of $9817.86. Round to the nearest whole percent.

Determine all possible rational solutions of the polynomial equation. - $f ( x ) = x ^ { 3 } - 6 x ^ { 2 } + 4 x - 24$

Solve the polynomial equation. - $( 2 x + 9 ) ^ { 2 } ( 8 - x ) ^ { 2 } = 0$

Graph the function. - $f ( x ) = \frac { x ^ { 2 } - x - 12 } { x + 4 }$ $Graph the function. - f ( x ) = \frac { x ^ { 2 } - x - 12 } { x + 4 }$

Match the polynomial function with the graph. - $y = x ^ { 4 } - 0.5 x ^ { 3 } - 15.5 x ^ { 2 } + 17 x + 14$

$f ( x ) = 0.62 x ^ { 3 } - 5 x ^ { 2 } + 11 x + 8$

Suppose a cost-benefit model is given b $y = \frac { 7.7 x } { 100 - x }$ where y is the cost in thousands of dollars for removing x percent of a given pollutant. Find the cost of removing 45% to the nearest dollar.

Use graphical methods to find any turning points of the graph of the function. - $f ( x ) = \frac { x ^ { 2 } - 8 x + 16 } { x - 5 }$

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Additional Topics With Functions

Exponential and Logarithmic Functions

Systems of Equations and Matrices

Special Topics in Algebra

Filters

Exam 6: Higher-Degree Polynomial and Rational Functions

Determine whether the polynomial function is cubic or quartic. -

Use synthetic division to find the quotient and remainder. - (2x3+3x2+4x−10)÷(x+1)\left( 2 x ^ { 3 } + 3 x ^ { 2 } + 4 x - 10 \right) \div ( x + 1 )(2x3+3x2+4x−10)÷(x+1)

2x3+9x2−27x−54>02 x ^ { 3 } + 9 x ^ { 2 } - 27 x - 54 > 02x3+9x2−27x−54>0

Use algebraic and/or graphical methods to solve the inequality. - (x+1)(x−3)(x−8)>0( x + 1 ) ( x - 3 ) ( x - 8 ) > 0(x+1)(x−3)(x−8)>0

Provide an appropriate response. -If Q varies inversely as the square roo R and Q=2 when R=9R \text { and } Q = 2 \text { when } R = 9R and Q=2 when R=9 , what is Q when R is 16?

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions. - 7x4+9x3−26x2−36x−8=0;−17 x ^ { 4 } + 9 x ^ { 3 } - 26 x ^ { 2 } - 36 x - 8 = 0 ; - 17x4+9x3−26x2−36x−8=0;−1

Use the graph of f(x) to solve the inequality. - f(x)<0f(x)<0f(x)<0

Use algebraic and/or graphical methods to solve the inequality. - (x+7)(x+6)(x−5)<0( x + 7 ) ( x + 6 ) ( x - 5 ) < 0(x+7)(x+6)(x−5)<0

Give the equations of any vertical asymptotes for the graphs of the rational functions. - f(x)=5x+25x−3f ( x ) = \frac { 5 x + 2 } { 5 x - 3 }f(x)=5x−35x+2​

The future value of $7000 invested for 5 years at rate r, compounded annually, is given by S=7000(1+r)5S = 7000 ( 1 + r ) ^ { 5 }S=7000(1+r)5 Find the rate r, as a percent, that gives a future value of $9817.86. Round to the nearest whole percent.

Determine all possible rational solutions of the polynomial equation. - f(x)=x3−6x2+4x−24f ( x ) = x ^ { 3 } - 6 x ^ { 2 } + 4 x - 24f(x)=x3−6x2+4x−24

Solve the polynomial equation. - (2x+9)2(8−x)2=0( 2 x + 9 ) ^ { 2 } ( 8 - x ) ^ { 2 } = 0(2x+9)2(8−x)2=0

Graph the function. - f(x)=x2−x−12x+4f ( x ) = \frac { x ^ { 2 } - x - 12 } { x + 4 }f(x)=x+4x2−x−12​

Match the polynomial function with the graph. - y=x4−0.5x3−15.5x2+17x+14y = x ^ { 4 } - 0.5 x ^ { 3 } - 15.5 x ^ { 2 } + 17 x + 14y=x4−0.5x3−15.5x2+17x+14

f(x)=0.62x3−5x2+11x+8f ( x ) = 0.62 x ^ { 3 } - 5 x ^ { 2 } + 11 x + 8f(x)=0.62x3−5x2+11x+8

Suppose a cost-benefit model is given b y=7.7x100−xy = \frac { 7.7 x } { 100 - x }y=100−x7.7x​ where y is the cost in thousands of dollars for removing x percent of a given pollutant. Find the cost of removing 45% to the nearest dollar.

Use graphical methods to find any turning points of the graph of the function. - f(x)=x2−8x+16x−5f ( x ) = \frac { x ^ { 2 } - 8 x + 16 } { x - 5 }f(x)=x−5x2−8x+16​

Functions, Graphs, and Models; Linear Functions

Linear Models, Equations, and Inequalities

Quadratic, Piecewise-Defined, and Power Functions

Additional Topics With Functions

Exponential and Logarithmic Functions

Systems of Equations and Matrices

Special Topics in Algebra

Filters

Use synthetic division to find the quotient and remainder. - $\left( 2 x ^ { 3 } + 3 x ^ { 2 } + 4 x - 10 \right) \div ( x + 1 )$

$2 x ^ { 3 } + 9 x ^ { 2 } - 27 x - 54 > 0$

Use algebraic and/or graphical methods to solve the inequality. - $( x + 1 ) ( x - 3 ) ( x - 8 ) > 0$

Provide an appropriate response. -If Q varies inversely as the square roo $R \text { and } Q = 2 \text { when } R = 9$ , what is Q when R is 16?

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions. - $7 x ^ { 4 } + 9 x ^ { 3 } - 26 x ^ { 2 } - 36 x - 8 = 0 ; - 1$

Use the graph of f(x) to solve the inequality. - $f(x)<0$

Use algebraic and/or graphical methods to solve the inequality. - $( x + 7 ) ( x + 6 ) ( x - 5 ) < 0$

Give the equations of any vertical asymptotes for the graphs of the rational functions. - $f ( x ) = \frac { 5 x + 2 } { 5 x - 3 }$

The future value of $7000 invested for 5 years at rate r, compounded annually, is given by $S = 7000 ( 1 + r ) ^ { 5 }$ Find the rate r, as a percent, that gives a future value of $9817.86. Round to the nearest whole percent.

Determine all possible rational solutions of the polynomial equation. - $f ( x ) = x ^ { 3 } - 6 x ^ { 2 } + 4 x - 24$

Solve the polynomial equation. - $( 2 x + 9 ) ^ { 2 } ( 8 - x ) ^ { 2 } = 0$

Graph the function. - $f ( x ) = \frac { x ^ { 2 } - x - 12 } { x + 4 }$ $Graph the function. - f ( x ) = \frac { x ^ { 2 } - x - 12 } { x + 4 }$

Match the polynomial function with the graph. - $y = x ^ { 4 } - 0.5 x ^ { 3 } - 15.5 x ^ { 2 } + 17 x + 14$

$f ( x ) = 0.62 x ^ { 3 } - 5 x ^ { 2 } + 11 x + 8$

Suppose a cost-benefit model is given b $y = \frac { 7.7 x } { 100 - x }$ where y is the cost in thousands of dollars for removing x percent of a given pollutant. Find the cost of removing 45% to the nearest dollar.

Use graphical methods to find any turning points of the graph of the function. - $f ( x ) = \frac { x ^ { 2 } - 8 x + 16 } { x - 5 }$