Question 1

$f ( x ) = 4.5 x ^ { 3 } + 12 x ^ { 2 } - 82$

Accepted Answer

A)   [-2,8]  by  [-250,150] 
B)   [-5,5]  by  [-200,50] 
C)   [-100,100]  by  [-10,10] 
D)   [-6,6]  by  [-50,100] 
A)   [-2,8]  by  [-250,150] 
B)   [-5,5]  by  [-200,50] 
C)   [-100,100]  by  [-10,10] 
D)   [-6,6]  by  [-50,100] B

Question 2

Match the polynomial function with the graph.
-$y = - x ^ { 4 } + 0.5 x ^ { 3 } + 15.5 x ^ { 2 } - 13 x - 16$

Accepted Answer

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

Question 3

Provide an appropriate response.
-Which function has no horizontal asymptote? Why? a. $f ( x ) = \frac { 2 x + 1 } { x - 2 }$
b. $f ( x ) = \frac { x ^ { 3 } } { 3 x ^ { 2 } + 1 }$
c. $f ( x ) = \frac { 6 x } { x ^ { 2 } - 16 }$
d. $f ( x ) = \frac { 8 } { ( x + 4 ) ( x - 3 ) }$

Accepted Answer

A)  a. The degree of the numerator is equal to the degree of the denominator. 
B)  d. The numerator is never equal to 0. 
C)  b. The degree of the numerator is greater than the degree of the denominator. 
D)  c. The degree of the numerator is less than the degree of the denominator. 
A)  a. The degree of the numerator is equal to the degree of the denominator. 
B)  d. The numerator is never equal to 0. 
C)  b. The degree of the numerator is greater than the degree of the denominator. 
D)  c. The degree of the numerator is less than the degree of the denominator. C

Question 4

Choose the graph that satisfies the given conditions.
-Degree 3 with one x $x \text {-intercept }$ intercept and a positive leading coefficient

Accepted Answer

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

Question 5

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions.
-$$x ^ { 4 } + 15 x ^ { 3 } + 49 x ^ { 2 } - 15 x - 50 = 0 ; 1$$

Accepted Answer

A)  $- 1,5,10$ 
B)  $- 5 , - 1,10$ 
C)  $- 10 , - 5,1$ 
D)  $- 10 , - 5 , - 1$ 
A)  $- 1,5,10$ 
B)  $- 5 , - 1,10$ 
C)  $- 10 , - 5,1$ 
D)  $- 10 , - 5 , - 1$

Question 6

The monthly sales volume y (in thousands of dollars) is related to monthly advertising expenditures x (in thousands of dollars) according to the equation $y = \frac { 100 x } { x + 10 }$ Spending how much money on advertising will
Result in sales of at least $50,000 per month?

Accepted Answer

A)  At least $5000 
B)  Between $5000 and $10,000 
C)  At least $10,000 
D)  At least $7500 
A)  At least $5000 
B)  Between $5000 and $10,000 
C)  At least $10,000 
D)  At least $7500

Question 7

$1 - \frac { 3 } { 2 x } = \frac { 7 } { 4 }$

Accepted Answer

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

Question 8

Accepted Answer

A)   -3.5,-2.5,1.5 
B)   -1.5,3.5 
C)   -1.5,2.5,3.5 
D)   -3.5,1.5 
A)   -3.5,-2.5,1.5 
B)   -1.5,3.5 
C)   -1.5,2.5,3.5 
D)   -3.5,1.5

Question 9

Use graphical methods to find any turning points of the graph of the function.
-$$y = \frac { 6 x } { x ^ { 2 } + 1 }$$

Accepted Answer

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

Question 10

$3 + \frac { 23 } { x } - \frac { 8 } { x ^ { 2 } } \leq 0$

Accepted Answer

A)  $\frac { 1 } { 3 } \leq x \leq 8$ 
B)  $- 8 \leq x < 0 \text { or } 0 < x \leq \frac { 1 } { 3 }$ 
C)  $x \leq - 8 \text { or } x \geq \frac { 1 } { 3 }$ 
D)  $- 8 \leq x \leq \frac { 1 } { 3 }$ 
A)  $\frac { 1 } { 3 } \leq x \leq 8$ 
B)  $- 8 \leq x < 0 \text { or } 0 < x \leq \frac { 1 } { 3 }$ 
C)  $x \leq - 8 \text { or } x \geq \frac { 1 } { 3 }$ 
D)  $- 8 \leq x \leq \frac { 1 } { 3 }$

Question 11

If the price for a product is given by $p = 6400 - x ^ { 2 }$, where $x$ is the number of units sold, then the revenue is given by $R = p x = 6400 x - x ^ { 3 }$. How many units must be sold to give zero revenue?

Accepted Answer

A)  6400 
B)  0, 6400 
C)  0, 80 
D)  0 
A)  6400 
B)  0, 6400 
C)  0, 80 
D)  0

Question 12

$\frac { x + 17 } { x + 4 } < 4$

Accepted Answer

A)  $- 4  \frac { 1 } { 3 }$ 
C)  $x  4$ 
D)  No solution 
A)  $- 4  \frac { 1 } { 3 }$ 
C)  $x  4$ 
D)  No solution

Question 13

Use factoring by grouping to solve the equation.
-$$x ^ { 3 } + 2 x ^ { 2 } - 16 x - 32 = 0$$

Accepted Answer

A)  $- 4 , - 2,2$ 
B)  $2 , - 4,4$ 
C)  $- 2,2,4$ 
D)  $- 2 , - 4,4$ 
A)  $- 4 , - 2,2$ 
B)  $2 , - 4,4$ 
C)  $- 2,2,4$ 
D)  $- 2 , - 4,4$

Question 14

Use graphical methods to find any turning points of the graph of the function.
-$$f ( x ) = \frac { 1 } { x ^ { 2 } - 1 }$$

Accepted Answer

A)  $( 1,0 ) , ( 0 , - 1 ) , ( - 1,0 )$ 
B)  $( 1,0 ) , ( - 1,0 )$ 
C)  $( 0 , - 1 )$ 
D)  No turning points 
A)  $( 1,0 ) , ( 0 , - 1 ) , ( - 1,0 )$ 
B)  $( 1,0 ) , ( - 1,0 )$ 
C)  $( 0 , - 1 )$ 
D)  No turning points

Question 15

For the given rational function, find all values of x for which y has the indicated value.
-$$y = 8 x + \frac { 15 } { x } ; \quad y = 26$$

Accepted Answer

A)  $\frac { 3 } { 4 } , \frac { 5 } { 2 }$ 
B)  $\frac { 2 } { 3 } , \frac { 4 } { 5 }$ 
C)  $\frac { 3 } { 2 } , \frac { 5 } { 4 }$ 
D)  $\frac { 4 } { 3 } , \frac { 2 } { 5 }$ 
A)  $\frac { 3 } { 4 } , \frac { 5 } { 2 }$ 
B)  $\frac { 2 } { 3 } , \frac { 4 } { 5 }$ 
C)  $\frac { 3 } { 2 } , \frac { 5 } { 4 }$ 
D)  $\frac { 4 } { 3 } , \frac { 2 } { 5 }$

Question 16

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

Accepted Answer

A)  $- 1  1$ 
B)  $1 < x < 2$ 
C)  $x < - 1$ or $0 < x < 1$ 
D)  $- 1 < x < 0$ or $1 < x < 2$ 
A)  $- 1  1$ 
B)  $1 < x < 2$ 
C)  $x < - 1$ or $0 < x < 1$ 
D)  $- 1 < x < 0$ or $1 < x < 2$

Question 17

A rectangular piece of cardboard measuring 20 inches by 39 inches is to be made into a box with an open top by cutting equal size squares from each corner and folding up the sides. Let x represent the length of a side of each
Such square. What is the maximum volume of this box? If necessary, round to 2 decimal places.

Accepted Answer

A)  $1364.09$ in. $^ { 3 }$ 
B)  $29,578.83$ in. 3 
C)  $1490.83$ in. 3 
D)  $631.5 \mathrm { in } ^ { 3 }$ 
A)  $1364.09$ in. $^ { 3 }$ 
B)  $29,578.83$ in. 3 
C)  $1490.83$ in. 3 
D)  $631.5 \mathrm { in } ^ { 3 }$

Question 18

$4 x ^ { 4 } + 3 x ^ { 3 } - 65 x ^ { 2 } - 48 x + 16 = 0 ; - 4$

Accepted Answer

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

Question 19

Solve the equation exactly in the complex number system.
-$$x ^ { 3 } - 6 x ^ { 2 } + x - 6 = 0$$

Accepted Answer

A)  $x = \pm 1 , x = 6$ 
B)  $x = 6 , x = \pm i$ 
C)  $x = \pm 6 , x = 1$ 
D)  $x = - 6 , x = \pm i$ 
A)  $x = \pm 1 , x = 6$ 
B)  $x = 6 , x = \pm i$ 
C)  $x = \pm 6 , x = 1$ 
D)  $x = - 6 , x = \pm i$

Question 20

Find all rational zeros of the polynomial function.
-$$f ( x ) = - 2 x ^ { 3 } - 4 x ^ { 2 } + 2 x + 4$$

Accepted Answer

A)  $1,2 , - 1$ 
B)  $- 1,2 , - 1$ 
C)  $- 1 , - 2,1$ 
D)  $1 , - 2,1$ 
A)  $1,2 , - 1$ 
B)  $- 1,2 , - 1$ 
C)  $- 1 , - 2,1$ 
D)  $1 , - 2,1$

$f ( x ) = 4.5 x ^ { 3 } + 12 x ^ { 2 } - 82$

Match the polynomial function with the graph. - $y = - x ^ { 4 } + 0.5 x ^ { 3 } + 15.5 x ^ { 2 } - 13 x - 16$

Provide an appropriate response. -Which function has no horizontal asymptote? Why? a. $f ( x ) = \frac { 2 x + 1 } { x - 2 }$ b. $f ( x ) = \frac { x ^ { 3 } } { 3 x ^ { 2 } + 1 }$ c. $f ( x ) = \frac { 6 x } { x ^ { 2 } - 16 }$ d. $f ( x ) = \frac { 8 } { ( x + 4 ) ( x - 3 ) }$

Choose the graph that satisfies the given conditions. -Degree 3 with one x $x \text {-intercept }$ intercept and a positive leading coefficient

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions. - $x ^ { 4 } + 15 x ^ { 3 } + 49 x ^ { 2 } - 15 x - 50 = 0 ; 1$

The monthly sales volume y (in thousands of dollars) is related to monthly advertising expenditures x (in thousands of dollars) according to the equation $y = \frac { 100 x } { x + 10 }$ Spending how much money on advertising will Result in sales of at least $50,000 per month?

$1 - \frac { 3 } { 2 x } = \frac { 7 } { 4 }$

Use graphical methods to find any turning points of the graph of the function. - $y = \frac { 6 x } { x ^ { 2 } + 1 }$

$3 + \frac { 23 } { x } - \frac { 8 } { x ^ { 2 } } \leq 0$

If the price for a product is given by $p = 6400 - x ^ { 2 }$ , where $x$ is the number of units sold, then the revenue is given by $R = p x = 6400 x - x ^ { 3 }$ . How many units must be sold to give zero revenue?

$\frac { x + 17 } { x + 4 } < 4$

Use factoring by grouping to solve the equation. - $x ^ { 3 } + 2 x ^ { 2 } - 16 x - 32 = 0$

Use graphical methods to find any turning points of the graph of the function. - $f ( x ) = \frac { 1 } { x ^ { 2 } - 1 }$

For the given rational function, find all values of x for which y has the indicated value. - $y = 8 x + \frac { 15 } { x } ; \quad y = 26$

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

$4 x ^ { 4 } + 3 x ^ { 3 } - 65 x ^ { 2 } - 48 x + 16 = 0 ; - 4$

Solve the equation exactly in the complex number system. - $x ^ { 3 } - 6 x ^ { 2 } + x - 6 = 0$

Find all rational zeros of the polynomial function. - $f ( x ) = - 2 x ^ { 3 } - 4 x ^ { 2 } + 2 x + 4$

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

f(x)=4.5x3+12x2−82f ( x ) = 4.5 x ^ { 3 } + 12 x ^ { 2 } - 82f(x)=4.5x3+12x2−82

Match the polynomial function with the graph. - y=−x4+0.5x3+15.5x2−13x−16y = - x ^ { 4 } + 0.5 x ^ { 3 } + 15.5 x ^ { 2 } - 13 x - 16y=−x4+0.5x3+15.5x2−13x−16

Choose the graph that satisfies the given conditions. -Degree 3 with one x x-intercept x \text {-intercept }x-intercept intercept and a positive leading coefficient

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions. - x4+15x3+49x2−15x−50=0;1x ^ { 4 } + 15 x ^ { 3 } + 49 x ^ { 2 } - 15 x - 50 = 0 ; 1x4+15x3+49x2−15x−50=0;1

The monthly sales volume y (in thousands of dollars) is related to monthly advertising expenditures x (in thousands of dollars) according to the equation y=100xx+10y = \frac { 100 x } { x + 10 }y=x+10100x​ Spending how much money on advertising will Result in sales of at least $50,000 per month?

1−32x=741 - \frac { 3 } { 2 x } = \frac { 7 } { 4 }1−2x3​=47​

Use graphical methods to find any turning points of the graph of the function. - y=6xx2+1y = \frac { 6 x } { x ^ { 2 } + 1 }y=x2+16x​

3+23x−8x2≤03 + \frac { 23 } { x } - \frac { 8 } { x ^ { 2 } } \leq 03+x23​−x28​≤0

If the price for a product is given by p=6400−x2p = 6400 - x ^ { 2 }p=6400−x2 , where xxx is the number of units sold, then the revenue is given by R=px=6400x−x3R = p x = 6400 x - x ^ { 3 }R=px=6400x−x3 . How many units must be sold to give zero revenue?

x+17x+4<4\frac { x + 17 } { x + 4 } < 4x+4x+17​<4

Use factoring by grouping to solve the equation. - x3+2x2−16x−32=0x ^ { 3 } + 2 x ^ { 2 } - 16 x - 32 = 0x3+2x2−16x−32=0

Use graphical methods to find any turning points of the graph of the function. - f(x)=1x2−1f ( x ) = \frac { 1 } { x ^ { 2 } - 1 }f(x)=x2−11​

For the given rational function, find all values of x for which y has the indicated value. - y=8x+15x;y=26y = 8 x + \frac { 15 } { x } ; \quad y = 26y=8x+x15​;y=26

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

4x4+3x3−65x2−48x+16=0;−44 x ^ { 4 } + 3 x ^ { 3 } - 65 x ^ { 2 } - 48 x + 16 = 0 ; - 44x4+3x3−65x2−48x+16=0;−4

Solve the equation exactly in the complex number system. - x3−6x2+x−6=0x ^ { 3 } - 6 x ^ { 2 } + x - 6 = 0x3−6x2+x−6=0

Find all rational zeros of the polynomial function. - f(x)=−2x3−4x2+2x+4f ( x ) = - 2 x ^ { 3 } - 4 x ^ { 2 } + 2 x + 4f(x)=−2x3−4x2+2x+4

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

$f ( x ) = 4.5 x ^ { 3 } + 12 x ^ { 2 } - 82$

Match the polynomial function with the graph. - $y = - x ^ { 4 } + 0.5 x ^ { 3 } + 15.5 x ^ { 2 } - 13 x - 16$

Choose the graph that satisfies the given conditions. -Degree 3 with one x $x \text {-intercept }$ intercept and a positive leading coefficient

One solution of a polynomial equation is given. Use synthetic division to find any remaining solutions. - $x ^ { 4 } + 15 x ^ { 3 } + 49 x ^ { 2 } - 15 x - 50 = 0 ; 1$

The monthly sales volume y (in thousands of dollars) is related to monthly advertising expenditures x (in thousands of dollars) according to the equation $y = \frac { 100 x } { x + 10 }$ Spending how much money on advertising will Result in sales of at least $50,000 per month?

$1 - \frac { 3 } { 2 x } = \frac { 7 } { 4 }$

Use graphical methods to find any turning points of the graph of the function. - $y = \frac { 6 x } { x ^ { 2 } + 1 }$

$3 + \frac { 23 } { x } - \frac { 8 } { x ^ { 2 } } \leq 0$

If the price for a product is given by $p = 6400 - x ^ { 2 }$ , where $x$ is the number of units sold, then the revenue is given by $R = p x = 6400 x - x ^ { 3 }$ . How many units must be sold to give zero revenue?

$\frac { x + 17 } { x + 4 } < 4$

Use factoring by grouping to solve the equation. - $x ^ { 3 } + 2 x ^ { 2 } - 16 x - 32 = 0$

Use graphical methods to find any turning points of the graph of the function. - $f ( x ) = \frac { 1 } { x ^ { 2 } - 1 }$

For the given rational function, find all values of x for which y has the indicated value. - $y = 8 x + \frac { 15 } { x } ; \quad y = 26$

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

$4 x ^ { 4 } + 3 x ^ { 3 } - 65 x ^ { 2 } - 48 x + 16 = 0 ; - 4$

Solve the equation exactly in the complex number system. - $x ^ { 3 } - 6 x ^ { 2 } + x - 6 = 0$

Find all rational zeros of the polynomial function. - $f ( x ) = - 2 x ^ { 3 } - 4 x ^ { 2 } + 2 x + 4$