Question 1

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

Accepted Answer

A)  $- 2  - 2$ 
C)  $- 4  1$ 
D)  $x < - 4$ or $- 2 < x < 1$ 
A)  $- 2  - 2$ 
C)  $- 4  1$ 
D)  $x < - 4$ or $- 2 < x < 1$

Question 2

State the degree and leading coefficient of the polynomial function.
-$$f ( x ) = - 4 ( x + 9 ) ^ { 2 } ( x - 9 ) ^ { 2 }$$

Accepted Answer

A)  Degree: 4 ; leading coefficient: 1 
B)  Degree: 2 ; leading coefficient: $- 4$ 
C)  Degree: 2; leading coefficient: 1 
D)  Degree: 4 ; leading coefficient: $- 4$ 
A)  Degree: 4 ; leading coefficient: 1 
B)  Degree: 2 ; leading coefficient: $- 4$ 
C)  Degree: 2; leading coefficient: 1 
D)  Degree: 4 ; leading coefficient: $- 4$

Question 3

Use algebraic and/or graphical methods to solve the inequality.
-$$( 2 x + 7 ) ( x - 8 ) ( 3 x - 7 ) \leq 0$$

Accepted Answer

A)  $x  8$ 
D)  $x \leq - \frac { 7 } { 2 }$ or $\frac { 7 } { 3 } \leq x \leq 8$ 
A)  $x  8$ 
D)  $x \leq - \frac { 7 } { 2 }$ or $\frac { 7 } { 3 } \leq x \leq 8$

Question 4

Graph the function.
-$f ( x ) = \frac { x ^ { 2 } - 9 } { x + 2 }$

Accepted Answer

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

Question 5

The revenue from the sale of a product is given by  $R = 1420 x - 17 x ^ { 2 } - x ^ { 3 }$ . If the sale of 10 units gives a total revenue of $11,500, use synthetic division to find another number of units that will give $11,500 in revenue.

Accepted Answer

A)  13 units 
B)  50 units 
C)  28 units 
D)  23 units 
A)  13 units 
B)  50 units 
C)  28 units 
D)  23 units

Question 6

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions.
-$$4 x ^ { 3 } + 13 x ^ { 2 } - 37 x - 10 = 0 ; 2$$

Accepted Answer

A)  $- 5 , - 1$ 
B)  5,1 
C)  $5 , \frac { 1 } { 4 }$ 
D)  $- 5 , - \frac { 1 } { 4 }$ 
A)  $- 5 , - 1$ 
B)  5,1 
C)  $5 , \frac { 1 } { 4 }$ 
D)  $- 5 , - \frac { 1 } { 4 }$

Question 7

The profit made when t units are sold, $t > 0$ is given by $P = t ^ { 2 } - 29 t + 204$ Determine the number of units to be sold in order for $\mathrm { P } < 0$ (a loss is taken).

Accepted Answer

A) $t 17 \text { units }$ B) $t > 0$ C) $12 \text { units } < t < 17 \text { units }$ D) t=12 units or t=17 units A) $t 17 \text { units }$ B) $t > 0$ C) $12 \text { units } < t < 17 \text { units }$ D) t=12 units or t=17 units

Question 8

Give the equations of any horizontal asymptotes for the graphs of the rational functions.
-$$g ( x ) = \frac { x ^ { 2 } + 8 x - 6 } { x - 6 }$$

Accepted Answer

A)  $y = - 8$ 
B)  none 
C)  $y = 2$ 
D)  $y = 6$ 
A)  $y = - 8$ 
B)  none 
C)  $y = 2$ 
D)  $y = 6$

Question 9

Use synthetic division to find the quotient and remainder.
-$$\left( 4 x ^ { 3 } - 25 x ^ { 2 } + 19 x + 30 \right) \div ( x - 5 )$$

Accepted Answer

A)  $4 x ^ { 2 } - 5 x - 6$ 
B)  $4 x - 5$ 
C)  $4 x ^ { 2 } - 5 x + 19$ 
D)  $- 4 x ^ { 2 } + 5 x - 6$ 
A)  $4 x ^ { 2 } - 5 x - 6$ 
B)  $4 x - 5$ 
C)  $4 x ^ { 2 } - 5 x + 19$ 
D)  $- 4 x ^ { 2 } + 5 x - 6$

Question 10

Solve the polynomial equation.
-$$( 2 x - 9 ) ( x + 4 ) ( x - 3 ) = 0$$

Accepted Answer

A)  $- \frac { 9 } { 2 } , 4 , - 3$ 
B)  108 
C)  $\frac { 9 } { 2 } , - 4,3$ 
D)  $9 , - 4,3$ 
A)  $- \frac { 9 } { 2 } , 4 , - 3$ 
B)  108 
C)  $\frac { 9 } { 2 } , - 4,3$ 
D)  $9 , - 4,3$

Question 11

Determine whether the given constant is a solution to the given polynomial equation.
-$- x ^ { 4 } - 2 x ^ { 2 } - 5 x + 34 = 0 ; 2$

Accepted Answer

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

Question 12

Find all rational zeros of the polynomial function.
-$$f ( x ) = x ^ { 3 } - 48 x - 128$$

Accepted Answer

A)  $4 , - 4,8$ 
B)  $- 4,4,8$ 
C)  $- 8 , - 4,4$ 
D)  $- 4 , - 4,8$ 
A)  $4 , - 4,8$ 
B)  $- 4,4,8$ 
C)  $- 8 , - 4,4$ 
D)  $- 4 , - 4,8$

Question 13

The table below gives the violent crime rate (per 100,000 people) for a particular state every five years from 1970 to 2010. 
$\begin{array} { c | c } 
\text { Year } & \text { Rate } \
\hline 1970 & 4.8 \
\hline 1975 & 5.0 \
\hline 1980 & 5.9 \
\hline 1985 & 7.3 \
\hline 1990 & 8.9 \
\hline 1995 & 10.4 \
\hline 2000 & 11.6 \
\hline 2005 & 12.3 \
\hline 2010 & 12.1
\end{array}$ 
Use technology to find the cubic function that is the best fit for this data, where x is the number of years after 1970. Use the model to estimate the violent crime rate for the year 2014.

Accepted Answer

A)  11.6 
B)  11.4 
C)  11.8 
D)  11 
A)  11.6 
B)  11.4 
C)  11.8 
D)  11

Question 14

$f ( x ) = 2 x ^ { 4 } + 2 x ^ { 3 } - 4 x ^ { 2 } - 3 x - 6$

Accepted Answer

A)   [-3,3]  by  [-3,4] 
B)   [-2,2]  by  [-10,-5] 
C)   [-3,3]  by  [-10,5] 
D)   [-5,5]  by  [-2,1] 
A)   [-3,3]  by  [-3,4] 
B)   [-2,2]  by  [-10,-5] 
C)   [-3,3]  by  [-10,5] 
D)   [-5,5]  by  [-2,1]

Question 15

Use factoring and the root method to solve the polynomial equation.
-$$x ^ { 4 } - 6 x ^ { 2 } + 9 = 0$$

Accepted Answer

A)  3 
B)  $- 3,3$ 
C)  $\sqrt { 3 }$ 
D)  $- \sqrt { 3 } , \sqrt { 3 }$ 
A)  3 
B)  $- 3,3$ 
C)  $\sqrt { 3 }$ 
D)  $- \sqrt { 3 } , \sqrt { 3 }$

Question 16

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

Accepted Answer

A) $x > 0$ B) $x 3$ D) $x < 0$ A) $x > 0$ B) $x 3$ D) $x < 0$

Question 17

Suppose a business can sell x gadgets for $p = 250 - 0.01 x$ dollars apiece, and it costs the business $c ( x ) = 1000 + 25 x$ dollars to produce the $x$ gadgets. Determine the production level and cost per gadget required to maximize profit.

Accepted Answer

A)  11,250 gadgets at $137.50 each 
B)  13,750 gadgets at $112.50 each 
C)  10,000 gadgets at $150.00 each 
D)  111 gadgets at $248.89 each 
A)  11,250 gadgets at $137.50 each 
B)  13,750 gadgets at $112.50 each 
C)  10,000 gadgets at $150.00 each 
D)  111 gadgets at $248.89 each

Question 18

Determine whether the polynomial function is cubic or quartic.
-

Accepted Answer

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

Question 19

Solve the equation exactly in the complex number system.
-$$x ^ { 3 } + 2 x ^ { 2 } + 49 x + 98 = 0$$

Accepted Answer

A)  $x = - 2 , x = 98 i , x = 49 i$ 
B)  $x = - \sqrt { 2 } , x = \pm 7 i$ 
C)  $x = - 2 , x = \pm \sqrt { 7 }$ 
D)  $x = - 2 , x = \pm 7 i$ 
A)  $x = - 2 , x = 98 i , x = 49 i$ 
B)  $x = - \sqrt { 2 } , x = \pm 7 i$ 
C)  $x = - 2 , x = \pm \sqrt { 7 }$ 
D)  $x = - 2 , x = \pm 7 i$

Question 20

$\frac { 7 } { x + 7 } > \frac { 5 } { x + 7 }$

Accepted Answer

A)  $x  - 7$ 
A)  $x  - 7$

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

State the degree and leading coefficient of the polynomial function. - $f ( x ) = - 4 ( x + 9 ) ^ { 2 } ( x - 9 ) ^ { 2 }$

Use algebraic and/or graphical methods to solve the inequality. - $( 2 x + 7 ) ( x - 8 ) ( 3 x - 7 ) \leq 0$

Graph the function. - $f ( x ) = \frac { x ^ { 2 } - 9 } { x + 2 }$ $Graph the function. - f ( x ) = \frac { x ^ { 2 } - 9 } { x + 2 }$

The revenue from the sale of a product is given by $R = 1420 x - 17 x ^ { 2 } - x ^ { 3 }$ . If the sale of 10 units gives a total revenue of $11,500, use synthetic division to find another number of units that will give $11,500 in revenue.

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions. - $4 x ^ { 3 } + 13 x ^ { 2 } - 37 x - 10 = 0 ; 2$

The profit made when t units are sold, $t > 0$ is given by $P = t ^ { 2 } - 29 t + 204$ Determine the number of units to be sold in order for $\mathrm { P } < 0$ (a loss is taken).

Give the equations of any horizontal asymptotes for the graphs of the rational functions. - $g ( x ) = \frac { x ^ { 2 } + 8 x - 6 } { x - 6 }$

Use synthetic division to find the quotient and remainder. - $\left( 4 x ^ { 3 } - 25 x ^ { 2 } + 19 x + 30 \right) \div ( x - 5 )$

Solve the polynomial equation. - $( 2 x - 9 ) ( x + 4 ) ( x - 3 ) = 0$

Determine whether the given constant is a solution to the given polynomial equation. - $- x ^ { 4 } - 2 x ^ { 2 } - 5 x + 34 = 0 ; 2$

Find all rational zeros of the polynomial function. - $f ( x ) = x ^ { 3 } - 48 x - 128$

$f ( x ) = 2 x ^ { 4 } + 2 x ^ { 3 } - 4 x ^ { 2 } - 3 x - 6$

Use factoring and the root method to solve the polynomial equation. - $x ^ { 4 } - 6 x ^ { 2 } + 9 = 0$

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

Suppose a business can sell x gadgets for $p = 250 - 0.01 x$ dollars apiece, and it costs the business $c ( x ) = 1000 + 25 x$ dollars to produce the $x$ gadgets. Determine the production level and cost per gadget required to maximize profit.

Determine whether the polynomial function is cubic or quartic. -

Solve the equation exactly in the complex number system. - $x ^ { 3 } + 2 x ^ { 2 } + 49 x + 98 = 0$

$\frac { 7 } { x + 7 } > \frac { 5 } { x + 7 }$

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

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

State the degree and leading coefficient of the polynomial function. - f(x)=−4(x+9)2(x−9)2f ( x ) = - 4 ( x + 9 ) ^ { 2 } ( x - 9 ) ^ { 2 }f(x)=−4(x+9)2(x−9)2

Use algebraic and/or graphical methods to solve the inequality. - (2x+7)(x−8)(3x−7)≤0( 2 x + 7 ) ( x - 8 ) ( 3 x - 7 ) \leq 0(2x+7)(x−8)(3x−7)≤0

Graph the function. - f(x)=x2−9x+2f ( x ) = \frac { x ^ { 2 } - 9 } { x + 2 }f(x)=x+2x2−9​

The revenue from the sale of a product is given by R=1420x−17x2−x3R = 1420 x - 17 x ^ { 2 } - x ^ { 3 }R=1420x−17x2−x3 . If the sale of 10 units gives a total revenue of $11,500, use synthetic division to find another number of units that will give $11,500 in revenue.

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions. - 4x3+13x2−37x−10=0;24 x ^ { 3 } + 13 x ^ { 2 } - 37 x - 10 = 0 ; 24x3+13x2−37x−10=0;2

The profit made when t units are sold, t>0t > 0t>0 is given by P=t2−29t+204P = t ^ { 2 } - 29 t + 204P=t2−29t+204 Determine the number of units to be sold in order for P<0\mathrm { P } < 0P<0 (a loss is taken).

Give the equations of any horizontal asymptotes for the graphs of the rational functions. - g(x)=x2+8x−6x−6g ( x ) = \frac { x ^ { 2 } + 8 x - 6 } { x - 6 }g(x)=x−6x2+8x−6​

Use synthetic division to find the quotient and remainder. - (4x3−25x2+19x+30)÷(x−5)\left( 4 x ^ { 3 } - 25 x ^ { 2 } + 19 x + 30 \right) \div ( x - 5 )(4x3−25x2+19x+30)÷(x−5)

Solve the polynomial equation. - (2x−9)(x+4)(x−3)=0( 2 x - 9 ) ( x + 4 ) ( x - 3 ) = 0(2x−9)(x+4)(x−3)=0

Determine whether the given constant is a solution to the given polynomial equation. - −x4−2x2−5x+34=0;2- x ^ { 4 } - 2 x ^ { 2 } - 5 x + 34 = 0 ; 2−x4−2x2−5x+34=0;2

Find all rational zeros of the polynomial function. - f(x)=x3−48x−128f ( x ) = x ^ { 3 } - 48 x - 128f(x)=x3−48x−128

f(x)=2x4+2x3−4x2−3x−6f ( x ) = 2 x ^ { 4 } + 2 x ^ { 3 } - 4 x ^ { 2 } - 3 x - 6f(x)=2x4+2x3−4x2−3x−6

Use factoring and the root method to solve the polynomial equation. - x4−6x2+9=0x ^ { 4 } - 6 x ^ { 2 } + 9 = 0x4−6x2+9=0

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

Suppose a business can sell x gadgets for p=250−0.01xp = 250 - 0.01 xp=250−0.01x dollars apiece, and it costs the business c(x)=1000+25xc ( x ) = 1000 + 25 xc(x)=1000+25x dollars to produce the xxx gadgets. Determine the production level and cost per gadget required to maximize profit.

Determine whether the polynomial function is cubic or quartic. -

Solve the equation exactly in the complex number system. - x3+2x2+49x+98=0x ^ { 3 } + 2 x ^ { 2 } + 49 x + 98 = 0x3+2x2+49x+98=0

7x+7>5x+7\frac { 7 } { x + 7 } > \frac { 5 } { x + 7 }x+77​>x+75​

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

State the degree and leading coefficient of the polynomial function. - $f ( x ) = - 4 ( x + 9 ) ^ { 2 } ( x - 9 ) ^ { 2 }$

Use algebraic and/or graphical methods to solve the inequality. - $( 2 x + 7 ) ( x - 8 ) ( 3 x - 7 ) \leq 0$

Graph the function. - $f ( x ) = \frac { x ^ { 2 } - 9 } { x + 2 }$ $Graph the function. - f ( x ) = \frac { x ^ { 2 } - 9 } { x + 2 }$

The revenue from the sale of a product is given by $R = 1420 x - 17 x ^ { 2 } - x ^ { 3 }$ . If the sale of 10 units gives a total revenue of $11,500, use synthetic division to find another number of units that will give $11,500 in revenue.

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions. - $4 x ^ { 3 } + 13 x ^ { 2 } - 37 x - 10 = 0 ; 2$

The profit made when t units are sold, $t > 0$ is given by $P = t ^ { 2 } - 29 t + 204$ Determine the number of units to be sold in order for $\mathrm { P } < 0$ (a loss is taken).

Give the equations of any horizontal asymptotes for the graphs of the rational functions. - $g ( x ) = \frac { x ^ { 2 } + 8 x - 6 } { x - 6 }$

Use synthetic division to find the quotient and remainder. - $\left( 4 x ^ { 3 } - 25 x ^ { 2 } + 19 x + 30 \right) \div ( x - 5 )$

Solve the polynomial equation. - $( 2 x - 9 ) ( x + 4 ) ( x - 3 ) = 0$

Determine whether the given constant is a solution to the given polynomial equation. - $- x ^ { 4 } - 2 x ^ { 2 } - 5 x + 34 = 0 ; 2$

Find all rational zeros of the polynomial function. - $f ( x ) = x ^ { 3 } - 48 x - 128$

$f ( x ) = 2 x ^ { 4 } + 2 x ^ { 3 } - 4 x ^ { 2 } - 3 x - 6$

Use factoring and the root method to solve the polynomial equation. - $x ^ { 4 } - 6 x ^ { 2 } + 9 = 0$

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

Suppose a business can sell x gadgets for $p = 250 - 0.01 x$ dollars apiece, and it costs the business $c ( x ) = 1000 + 25 x$ dollars to produce the $x$ gadgets. Determine the production level and cost per gadget required to maximize profit.

Solve the equation exactly in the complex number system. - $x ^ { 3 } + 2 x ^ { 2 } + 49 x + 98 = 0$

$\frac { 7 } { x + 7 } > \frac { 5 } { x + 7 }$