Question 1

For the given rational function, find all values of x for which y has the indicated value.
-$$y = 2 x + \frac { 24 } { x } ; \quad y = - 16$$

Accepted Answer

A)  $- 3 , - 4$ 
B)  $- 2 , - 6$ 
C)  2,6 
D)  $- \frac { 1 } { 2 } , - 6$ 
A)  $- 3 , - 4$ 
B)  $- 2 , - 6$ 
C)  2,6 
D)  $- \frac { 1 } { 2 } , - 6$

Question 2

$\frac { 2 x } { x + 1 } \leq \frac { 4 } { x - 5 }$

Accepted Answer

A)  $- 1 < x \leq \frac { 7 - \sqrt { 55 } } { 2 } \text { or } 5 < x \leq \frac { 7 + \sqrt { 55 } } { 2 }$ 
B)  $- 1 < x \leq \frac { 7 + \sqrt { 57 } } { 2 } \text { or } 5 < x \leq \frac { 7 - \sqrt { 57 } } { 2 }$ 
C)  $- 1 < x < \frac { 7 - \sqrt { 55 } } { 2 } \text { or } 5 < x < \frac { 7 + \sqrt { 57 } } { 2 }$ 
D)  $- 1 < x \leq \frac { 7 - \sqrt { 57 } } { 2 } \text { or } 5 < x \leq \frac { 7 + \sqrt { 57 } } { 2 }$ 
A)  $- 1 < x \leq \frac { 7 - \sqrt { 55 } } { 2 } \text { or } 5 < x \leq \frac { 7 + \sqrt { 55 } } { 2 }$ 
B)  $- 1 < x \leq \frac { 7 + \sqrt { 57 } } { 2 } \text { or } 5 < x \leq \frac { 7 - \sqrt { 57 } } { 2 }$ 
C)  $- 1 < x < \frac { 7 - \sqrt { 55 } } { 2 } \text { or } 5 < x < \frac { 7 + \sqrt { 57 } } { 2 }$ 
D)  $- 1 < x \leq \frac { 7 - \sqrt { 57 } } { 2 } \text { or } 5 < x \leq \frac { 7 + \sqrt { 57 } } { 2 }$

Question 3

State the degree and leading coefficient of the polynomial function.
-$$f ( x ) = 16 x ^ { 4 } - 5 x + 5$$

Accepted Answer

A)  Degree: 6; leading coefficient: 16 
B)  Degree: 5; leading coefficient: 16 
C)  Degree: 16; leading coefficient: 4 
D)  Degree: 4; leading coefficient: 16 
A)  Degree: 6; leading coefficient: 16 
B)  Degree: 5; leading coefficient: 16 
C)  Degree: 16; leading coefficient: 4 
D)  Degree: 4; leading coefficient: 16

Question 4

$\frac { 4 } { x + 7 } > \frac { 7 } { 9 }$

Accepted Answer

A)  $\frac { 13 } { 7 }  - \frac { 13 } { 7 }$ 
A)  $\frac { 13 } { 7 }  - \frac { 13 } { 7 }$

Question 5

Solve the polynomial equation by using the root method.
-$$3 x ^ { 4 } - 768 = 0$$

Accepted Answer

A)  $- 4$ 
B)  4,0 
C)  $4 , - 4$ 
D)  4 
A)  $- 4$ 
B)  4,0 
C)  $4 , - 4$ 
D)  4

Question 6

A new health food store runs an advertising campaign. Daily sales (in dollars) after x days of advertising are given by $S ( x ) = \frac { 2500 x + 8500 } { x + 1 }$ By sketching the graph of this function, answer the following questions. What is the horizontal asymptote of the graph?
What does this suggest about future sales? Explain your reasoning. If the advertising campaign costs $3200 per day, at
what point should it be discontinued? Why?

Accepted Answer

The horizontal asymptote is @#LAT-DLM& This sugges

Question 7

$x ^ { 4 } - 53 x ^ { 2 } + 196 < 0$

Accepted Answer

A)  $x  2$ 
B)  $- 7 < x < - 2 \text { or } 2 < x < 7$ 
C)  $- 7 < x < - 2$ 
D)  $- 7 < x < 7$ 
A)  $x  2$ 
B)  $- 7 < x < - 2 \text { or } 2 < x < 7$ 
C)  $- 7 < x < - 2$ 
D)  $- 7 < x < 7$

Question 8

Ariel, a marine biologist, models a population P of crabs, t days after being left to reproduce, with the function $\mathrm { P } ( \mathrm { t } ) = - 0.00003 \mathrm { t } ^ { 3 } + 0.008 \mathrm { t } ^ { 2 } + 3.5 \mathrm { t } + 600$ . Assuming that this model continues to be accurate, when will this population become extinct? (Round to the nearest day.)

Accepted Answer

A)  707 days 
B)  911 days 
C)  1512 days 
D)  547 days 
A)  707 days 
B)  911 days 
C)  1512 days 
D)  547 days

Question 9

Use the given graph of the polynomial function to estimate the x-intercepts.
-

Accepted Answer

A)  $- 2,1$ 
B)  $- 2,3$ 
C)  $- 2,1,3$ 
D)  $- 3,1,2$ 
A)  $- 2,1$ 
B)  $- 2,3$ 
C)  $- 2,1,3$ 
D)  $- 3,1,2$

Question 10

Use synthetic division to find the quotient and remainder.
-$$\left( x ^ { 3 } - 5 \right) \div ( x - 1 )$$

Accepted Answer

A)  $x ^ { 2 } + x + 1 + \frac { 5 } { x - 1 }$ 
B)  $x ^ { 2 } - x - 1$ 
C)  $x ^ { 3 } - x ^ { 2 } - x - 1$ 
D)  $x ^ { 2 } + x + 1 + \frac { - 4 } { x - 1 }$ 
A)  $x ^ { 2 } + x + 1 + \frac { 5 } { x - 1 }$ 
B)  $x ^ { 2 } - x - 1$ 
C)  $x ^ { 3 } - x ^ { 2 } - x - 1$ 
D)  $x ^ { 2 } + x + 1 + \frac { - 4 } { x - 1 }$

Question 11

$f ( x ) = \frac { x ^ { 2 } + 1 } { x ^ { 2 } }$

Accepted Answer

A)   (1,2) 
B)  No turning points 
C)   (-1,-2) 
D)   (0,0) 
A)   (1,2) 
B)  No turning points 
C)   (-1,-2) 
D)   (0,0)

Question 12

Suppose that a cost-benefit model is given by $f ( x ) = \frac { 3.5 x } { 100 - x }$ where f(x) is the cost in thousands of dollars of removing x percent of a given pollutant. What is the vertical asymptote of the graph of this function? What does this suggest about the possibility of removing all of the pollutant? Explain your
reasoning.

Accepted Answer

The vertical asymptote i @#LAT-DLM& This

Question 13

Give the equations of any vertical asymptotes for the graphs of the rational functions.
-$$f ( x ) = \frac { x - 1 } { x ^ { 2 } + 3 }$$

Accepted Answer

A)  $x = 1 , x = - 1$ 
B)  $x = 3$ 
C)  $x = - 3$ 
D)  None 
A)  $x = 1 , x = - 1$ 
B)  $x = 3$ 
C)  $x = - 3$ 
D)  None

Question 14

Determine a window that will provide a comprehensive graph of the polynomial function.
-$$y = 2 x ^ { 4 } + 2 x ^ { 3 } - 4 x ^ { 2 } - 3 x - 6$$

Accepted Answer

A)  $[ - 2,2 ]$ by $[ - 10 , - 5 ]$ 
B)  $[ - 3,3 ]$ by $[ - 10,5 ]$ 
C)  $[ - 5,5 ]$ by $[ - 5,5 ]$ 
D)  $[ - 10,10 ]$ by $[ - 8,8 ]$ 
A)  $[ - 2,2 ]$ by $[ - 10 , - 5 ]$ 
B)  $[ - 3,3 ]$ by $[ - 10,5 ]$ 
C)  $[ - 5,5 ]$ by $[ - 5,5 ]$ 
D)  $[ - 10,10 ]$ by $[ - 8,8 ]$

Question 15

Choose the graph that satisfies the given conditions.
-Polynomial of degree 4 with two distinc $\text { x-intercepts }$ s and a negative leading coefficient

Accepted Answer

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

Question 16

The price for a product is given by $p = 4050 - 0.5 x ^ { 2 }$ be sold to give positive revenue?
, where  x  is the number of units sold. How many units must

Accepted Answer

A)  $x  90 \text { units }$ 
C)  $0 \text { units } < x < 90 \text { units }$ 
D)  $0 \text { units } < x < 45 \text { units }$ 
A)  $x  90 \text { units }$ 
C)  $0 \text { units } < x < 90 \text { units }$ 
D)  $0 \text { units } < x < 45 \text { units }$

Question 17

Find one solution graphically and then find the remaining solutions using synthetic division.
-3x4 + 2x3 - 76x2 - 50x + 25 = 0

Accepted Answer

A)  -5, 5, -1, 13 
B)  5, -1, 13 
C)  5, -5, 1, - 13 
D)  5, -5, 1, -1 
A)  -5, 5, -1, 13 
B)  5, -1, 13 
C)  5, -5, 1, - 13 
D)  5, -5, 1, -1

Question 18

Choose the graph that satisfies the given conditions.
-Degree 4 with four x $\mathrm { x } \text {-intercepts }$ s and a negative leading coefficient

Accepted Answer

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

Question 19

Determine a window that will provide a comprehensive graph of the polynomial function.
-$$y = 3 x ^ { 3 } - 26 x ^ { 2 } + 18 x - 47$$

Accepted Answer

A)  $[ - 5,5 ]$ by $[ - 500,100 ]$ 
B)  $[ - 3,10 ]$ by $[ - 400,100 ]$ 
C)  $[ - 8,10 ]$ by $[ - 100,300 ]$ 
D)  $[ - 10,10 ]$ by $[ - 150,150 ]$ 
A)  $[ - 5,5 ]$ by $[ - 500,100 ]$ 
B)  $[ - 3,10 ]$ by $[ - 400,100 ]$ 
C)  $[ - 8,10 ]$ by $[ - 100,300 ]$ 
D)  $[ - 10,10 ]$ by $[ - 150,150 ]$

Question 20

State the degree and leading coefficient of the polynomial function.
-$$f ( x ) = 14 x ^ { 4 } + 3 x ^ { 3 } - 5$$

Accepted Answer

A)  Degree: 14; leading coefficient: 4 
B)  Degree: 8; leading coefficient: 14 
C)  Degree: 7; leading coefficient: 14 
D)  Degree: 4; leading coefficient: 14 
A)  Degree: 14; leading coefficient: 4 
B)  Degree: 8; leading coefficient: 14 
C)  Degree: 7; leading coefficient: 14 
D)  Degree: 4; leading coefficient: 14

For the given rational function, find all values of x for which y has the indicated value. - $y = 2 x + \frac { 24 } { x } ; \quad y = - 16$

$\frac { 2 x } { x + 1 } \leq \frac { 4 } { x - 5 }$

State the degree and leading coefficient of the polynomial function. - $f ( x ) = 16 x ^ { 4 } - 5 x + 5$

$\frac { 4 } { x + 7 } > \frac { 7 } { 9 }$

Solve the polynomial equation by using the root method. - $3 x ^ { 4 } - 768 = 0$

$x ^ { 4 } - 53 x ^ { 2 } + 196 < 0$

Use the given graph of the polynomial function to estimate the x-intercepts. -

Use synthetic division to find the quotient and remainder. - $\left( x ^ { 3 } - 5 \right) \div ( x - 1 )$

$f ( x ) = \frac { x ^ { 2 } + 1 } { x ^ { 2 } }$

Give the equations of any vertical asymptotes for the graphs of the rational functions. - $f ( x ) = \frac { x - 1 } { x ^ { 2 } + 3 }$

Determine a window that will provide a comprehensive graph of the polynomial function. - $y = 2 x ^ { 4 } + 2 x ^ { 3 } - 4 x ^ { 2 } - 3 x - 6$

Choose the graph that satisfies the given conditions. -Polynomial of degree 4 with two distinc $\text { x-intercepts }$ s and a negative leading coefficient

The price for a product is given by $p = 4050 - 0.5 x ^ { 2 }$ be sold to give positive revenue? , where x is the number of units sold. How many units must

Find one solution graphically and then find the remaining solutions using synthetic division. -3x4 + 2x3 - 76x2 - 50x + 25 = 0

Choose the graph that satisfies the given conditions. -Degree 4 with four x $\mathrm { x } \text {-intercepts }$ s and a negative leading coefficient

Determine a window that will provide a comprehensive graph of the polynomial function. - $y = 3 x ^ { 3 } - 26 x ^ { 2 } + 18 x - 47$

State the degree and leading coefficient of the polynomial function. - $f ( x ) = 14 x ^ { 4 } + 3 x ^ { 3 } - 5$

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

For the given rational function, find all values of x for which y has the indicated value. - y=2x+24x;y=−16y = 2 x + \frac { 24 } { x } ; \quad y = - 16y=2x+x24​;y=−16

2xx+1≤4x−5\frac { 2 x } { x + 1 } \leq \frac { 4 } { x - 5 }x+12x​≤x−54​

State the degree and leading coefficient of the polynomial function. - f(x)=16x4−5x+5f ( x ) = 16 x ^ { 4 } - 5 x + 5f(x)=16x4−5x+5

4x+7>79\frac { 4 } { x + 7 } > \frac { 7 } { 9 }x+74​>97​

Solve the polynomial equation by using the root method. - 3x4−768=03 x ^ { 4 } - 768 = 03x4−768=0

x4−53x2+196<0x ^ { 4 } - 53 x ^ { 2 } + 196 < 0x4−53x2+196<0

Use the given graph of the polynomial function to estimate the x-intercepts. -

Use synthetic division to find the quotient and remainder. - (x3−5)÷(x−1)\left( x ^ { 3 } - 5 \right) \div ( x - 1 )(x3−5)÷(x−1)

f(x)=x2+1x2f ( x ) = \frac { x ^ { 2 } + 1 } { x ^ { 2 } }f(x)=x2x2+1​

Give the equations of any vertical asymptotes for the graphs of the rational functions. - f(x)=x−1x2+3f ( x ) = \frac { x - 1 } { x ^ { 2 } + 3 }f(x)=x2+3x−1​

Determine a window that will provide a comprehensive graph of the polynomial function. - y=2x4+2x3−4x2−3x−6y = 2 x ^ { 4 } + 2 x ^ { 3 } - 4 x ^ { 2 } - 3 x - 6y=2x4+2x3−4x2−3x−6

Choose the graph that satisfies the given conditions. -Polynomial of degree 4 with two distinc x-intercepts \text { x-intercepts } x-intercepts s and a negative leading coefficient

The price for a product is given by p=4050−0.5x2p = 4050 - 0.5 x ^ { 2 }p=4050−0.5x2 be sold to give positive revenue? , where x is the number of units sold. How many units must

Find one solution graphically and then find the remaining solutions using synthetic division. -3x4 + 2x3 - 76x2 - 50x + 25 = 0

Choose the graph that satisfies the given conditions. -Degree 4 with four x x-intercepts \mathrm { x } \text {-intercepts }x-intercepts s and a negative leading coefficient

Determine a window that will provide a comprehensive graph of the polynomial function. - y=3x3−26x2+18x−47y = 3 x ^ { 3 } - 26 x ^ { 2 } + 18 x - 47y=3x3−26x2+18x−47

State the degree and leading coefficient of the polynomial function. - f(x)=14x4+3x3−5f ( x ) = 14 x ^ { 4 } + 3 x ^ { 3 } - 5f(x)=14x4+3x3−5

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

For the given rational function, find all values of x for which y has the indicated value. - $y = 2 x + \frac { 24 } { x } ; \quad y = - 16$

$\frac { 2 x } { x + 1 } \leq \frac { 4 } { x - 5 }$

State the degree and leading coefficient of the polynomial function. - $f ( x ) = 16 x ^ { 4 } - 5 x + 5$

$\frac { 4 } { x + 7 } > \frac { 7 } { 9 }$

Solve the polynomial equation by using the root method. - $3 x ^ { 4 } - 768 = 0$

$x ^ { 4 } - 53 x ^ { 2 } + 196 < 0$

Use synthetic division to find the quotient and remainder. - $\left( x ^ { 3 } - 5 \right) \div ( x - 1 )$

$f ( x ) = \frac { x ^ { 2 } + 1 } { x ^ { 2 } }$

Give the equations of any vertical asymptotes for the graphs of the rational functions. - $f ( x ) = \frac { x - 1 } { x ^ { 2 } + 3 }$

Determine a window that will provide a comprehensive graph of the polynomial function. - $y = 2 x ^ { 4 } + 2 x ^ { 3 } - 4 x ^ { 2 } - 3 x - 6$

Choose the graph that satisfies the given conditions. -Polynomial of degree 4 with two distinc $\text { x-intercepts }$ s and a negative leading coefficient

The price for a product is given by $p = 4050 - 0.5 x ^ { 2 }$ be sold to give positive revenue? , where x is the number of units sold. How many units must

Choose the graph that satisfies the given conditions. -Degree 4 with four x $\mathrm { x } \text {-intercepts }$ s and a negative leading coefficient

Determine a window that will provide a comprehensive graph of the polynomial function. - $y = 3 x ^ { 3 } - 26 x ^ { 2 } + 18 x - 47$

State the degree and leading coefficient of the polynomial function. - $f ( x ) = 14 x ^ { 4 } + 3 x ^ { 3 } - 5$