Question 1

Match the function with its graph.
-$$f ( x ) = \frac { x - 4 } { x + 5 }$$

Accepted Answer

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

Question 2

Predict the end behavior of the graph of the function.
-$$f ( x ) = 3.63 x ^ { 4 } + 6 x ^ { 2 } + x - 2$$

Accepted Answer

A)  Up on left side, down on right side 
B)  Down on left side, up on right side 
C)  Up on both sides 
D)  Down on both sides 
A)  Up on left side, down on right side 
B)  Down on left side, up on right side 
C)  Up on both sides 
D)  Down on both sides

Question 3

Suppose that the population of a certain city during a certain time period can be approximated by $P ( x ) = - 0.1 x ^ { 5 } + 3.5 x ^ { 4 } + 4000$ , where x is time in years since 2010. By sketching a graph of P(x), estimate during what time period the population of the city would be increasing.

Accepted Answer

A)  Between 2010 and 2024 
B)  Between 2015 and 2045 
C)  Between 2015 and 2038 
D)  Between 2010 and 2038 
A)  Between 2010 and 2024 
B)  Between 2015 and 2045 
C)  Between 2015 and 2038 
D)  Between 2010 and 2038

Question 4

Find all rational zeros of the polynomial function.
-$$f ( x ) = 4 x ^ { 3 } + 13 x ^ { 2 } - 37 x - 10$$

Accepted Answer

A)  $5 , - 2 , \frac { 1 } { 4 }$ 
B)  $5 , - 2,1$ 
C)  $- 5,2 , - \frac { 1 } { 4 }$ 
D)  $- 5,2 , - 1$ 
A)  $5 , - 2 , \frac { 1 } { 4 }$ 
B)  $5 , - 2,1$ 
C)  $- 5,2 , - \frac { 1 } { 4 }$ 
D)  $- 5,2 , - 1$

Question 5

A pharmaceutical company claims that the concentration of a drug in a patient's bloodstream will be at least  25 %  for 8 hours. Suppose that clinical tests show that the concentration of the drug (as a percent) thours after injection is given by $C ( t ) = \frac { 900 t } { 6 t ^ { 2 } + 30 }$
During what time period is the concentration at least  25 %  ?

Accepted Answer

A)  $1 \text { hours } \leq t \leq 5 \text { hours }$ 
B)  $2 \text { hours } \leq t \leq 10 \text { hours }$ 
C)  $1 \text { hours } \leq t \leq 9 \text { hours }$ 
D)  $0 \text { hours } \leq t \leq 8 \text { hours }$ 
A)  $1 \text { hours } \leq t \leq 5 \text { hours }$ 
B)  $2 \text { hours } \leq t \leq 10 \text { hours }$ 
C)  $1 \text { hours } \leq t \leq 9 \text { hours }$ 
D)  $0 \text { hours } \leq t \leq 8 \text { hours }$

Question 6

$x ^ { 4 } - 81 = 0$

Accepted Answer

A)   6,-6 
B)   9,-9 
C)   3,-3 
D)   18,-18 
A)   6,-6 
B)   9,-9 
C)   3,-3 
D)   18,-18

Question 7

Use analytical methods to solve the equation.
-$$\frac { 8 } { x + 6 } = - \frac { 7 } { 9 }$$

Accepted Answer

A)  No solution 
B)  $- \frac { 110 } { 9 }$ 
C)  $- \frac { 30 } { 7 }$ 
D)  $- \frac { 114 } { 7 }$ 
A)  No solution 
B)  $- \frac { 110 } { 9 }$ 
C)  $- \frac { 30 } { 7 }$ 
D)  $- \frac { 114 } { 7 }$

Question 8

Use the given graph of the polynomial function to state whether the leading coefficient is positive or negative and whether the polynomial function is cubic or quartic.
-

Accepted Answer

A)  Negative; Cubic 
B)  Positive; Cubic 
C)  Negative; Quartic 
D)  Positive; Quartic 
A)  Negative; Cubic 
B)  Positive; Cubic 
C)  Negative; Quartic 
D)  Positive; Quartic

Question 9

$\frac { 3 x + 6 } { 5 x ^ { 2 } + 5 } > 0$

Accepted Answer

A) $x > 0$ B) $x > - 2$ C) $x < - \frac { 1 } { 2 }$ D) $x < - 2$ A) $x > 0$ B) $x > - 2$ C) $x < - \frac { 1 } { 2 }$ D) $x < - 2$

Question 10

Use a graphing calculator to estimate the local maximum and local minimum values of the function to the nearest
hundredth.
-$$y = 3 x ^ { 3 } - 4 x ^ { 2 } - 6 x + 2$$

Accepted Answer

A)  Local max: $( - 0.48,3.63 )$; local min: $( 1.38 , - 6.01 )$ 
B)  Local max: (-0.48, 3.68); local min: $( 1.38 , - 6.15 )$ 
C)  Local max: $( - 0.44,3.61 )$; local min: $( 1.45 , - 5.97 )$ 
D)  Local max: $( - 6.01,1.38 )$; local min: $( 3.63 , - 0.48 )$ 
A)  Local max: $( - 0.48,3.63 )$; local min: $( 1.38 , - 6.01 )$ 
B)  Local max: (-0.48, 3.68); local min: $( 1.38 , - 6.15 )$ 
C)  Local max: $( - 0.44,3.61 )$; local min: $( 1.45 , - 5.97 )$ 
D)  Local max: $( - 6.01,1.38 )$; local min: $( 3.63 , - 0.48 )$

Question 11

Use the given graph of the polynomial function to state whether the leading coefficient is positive or negative and whether the polynomial function is cubic or quartic.
-

Accepted Answer

A)  Negative; Cubic 
B)  Negative; Quartic 
C)  Positive; Quartic 
D)  Positive; Cubic 
A)  Negative; Cubic 
B)  Negative; Quartic 
C)  Positive; Quartic 
D)  Positive; Cubic

Question 12

Determine all possible rational solutions of the polynomial equation.
-$$f ( x ) = - 2 x ^ { 4 } + 4 x ^ { 3 } + 5 x ^ { 2 } + 18$$

Accepted Answer

A)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 2 , \pm 3 , \pm 6 , \pm 9 , \pm 18$ 
B)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 2 , \pm 3 , \pm \frac { 3 } { 2 } , \pm 6 , \pm 9 , \pm \frac { 9 } { 2 } , \pm 18$ 
C)  $\pm 1 , \pm 2 , \pm 3 , \pm 6 , \pm 9 , \pm 18$ 
D)  $\pm 1 , \pm 2 , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 6 } , \pm \frac { 1 } { 9 } , \pm \frac { 1 } { 18 }$ 
A)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 2 , \pm 3 , \pm 6 , \pm 9 , \pm 18$ 
B)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 2 , \pm 3 , \pm \frac { 3 } { 2 } , \pm 6 , \pm 9 , \pm \frac { 9 } { 2 } , \pm 18$ 
C)  $\pm 1 , \pm 2 , \pm 3 , \pm 6 , \pm 9 , \pm 18$ 
D)  $\pm 1 , \pm 2 , \pm \frac { 1 } { 2 } , \pm \frac { 1 } { 3 } , \pm \frac { 1 } { 6 } , \pm \frac { 1 } { 9 } , \pm \frac { 1 } { 18 }$

Question 13

Use the graph of the polynomial function f(x) to solve f( $$f ( x ) \text { to solve } f ( x ) = 0$$
-

Accepted Answer

A)  0,2 
B)  $- 2$ 
C)  $- 2,0$ 
D)  0 
A)  0,2 
B)  $- 2$ 
C)  $- 2,0$ 
D)  0

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)  $( - 1,0.5 )$ 
B)  $( - 1,0.5 ) , ( 0,1 ) , ( 1,0.5 )$ 
C)  $( 1,0.5 )$ 
D)  $( 0,1 )$ 
A)  $( - 1,0.5 )$ 
B)  $( - 1,0.5 ) , ( 0,1 ) , ( 1,0.5 )$ 
C)  $( 1,0.5 )$ 
D)  $( 0,1 )$

Question 15

Choose the graph that satisfies the given conditions.
-Polynomial of degree 3 with three distinct x $\text { x-intercepts a }$ nd a positive leading coefficient

Accepted Answer

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

Question 16

An architect needs to design a rectangular room with an area of  97 ft2 . What dimensions should he use in order to minimize the perimeter?

Accepted Answer

A)   19.4 ft x 97 ft 
B)   9.85 ft x 24.25 ft 
C)   24.25 ft x 24.25 ft 
D)   9.85 ft x 9.85 ft 
A)   19.4 ft x 97 ft 
B)   9.85 ft x 24.25 ft 
C)   24.25 ft x 24.25 ft 
D)   9.85 ft x 9.85 ft

Question 17

Find the cubic or quartic function that models the data in the table.
-$\begin{array}{c|cccc}
x & -5 & 0 & 2 & 3 \
\hline y & -60 & 5 & 3 & 10
\end{array} \text { (Cubic) }$

Accepted Answer

A)  $y = 0.58 x ^ { 3 } - 0.25 x ^ { 2 } - 2.83 x + 5.00$ 
B)  $y = 0.49 x ^ { 3 } - 0.25 x ^ { 2 } + 2.83 x + 5.00$ 
C)  $y = 0.49 x ^ { 3 } - 0.25 x ^ { 2 } - 2.83 x + 5.00$ 
D)  $y = 0.58 x ^ { 3 } + 0.25 x ^ { 2 } - 2.83 x + 5.00$ 
A)  $y = 0.58 x ^ { 3 } - 0.25 x ^ { 2 } - 2.83 x + 5.00$ 
B)  $y = 0.49 x ^ { 3 } - 0.25 x ^ { 2 } + 2.83 x + 5.00$ 
C)  $y = 0.49 x ^ { 3 } - 0.25 x ^ { 2 } - 2.83 x + 5.00$ 
D)  $y = 0.58 x ^ { 3 } + 0.25 x ^ { 2 } - 2.83 x + 5.00$

Question 18

Determine whether the given constant is a solution to the given polynomial equation.
-$- 9 x ^ { 3 } + x ^ { 2 } - 3 x + 6 = 0 ; - 1$

Accepted Answer

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

Question 19

Use graphical methods to find any turning points of the graph of the function.
-$$f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 3 }$$

Accepted Answer

A)  (0, 0) and (3, 0.75) 
B)  No turning points 
C)  (3, 0.75) 
D)  (0, 0) 
A)  (0, 0) and (3, 0.75) 
B)  No turning points 
C)  (3, 0.75) 
D)  (0, 0)

Question 20

Solve the equation exactly in the complex number system.
-$$x ^ { 3 } + 4 x ^ { 2 } - 2 x - 8 = 0$$

Accepted Answer

A)  $x = - \sqrt { 4 } , x = \pm 2$ 
B)  $x = - 4 , x = \pm 2$ 
C)  $x = - 4 , x = \pm \sqrt { 2 }$ 
D)  $x = - \sqrt { 4 } , x = \pm \sqrt { 2 }$ 
A)  $x = - \sqrt { 4 } , x = \pm 2$ 
B)  $x = - 4 , x = \pm 2$ 
C)  $x = - 4 , x = \pm \sqrt { 2 }$ 
D)  $x = - \sqrt { 4 } , x = \pm \sqrt { 2 }$

Match the function with its graph. - $f ( x ) = \frac { x - 4 } { x + 5 }$

Predict the end behavior of the graph of the function. - $f ( x ) = 3.63 x ^ { 4 } + 6 x ^ { 2 } + x - 2$

Suppose that the population of a certain city during a certain time period can be approximated by $P ( x ) = - 0.1 x ^ { 5 } + 3.5 x ^ { 4 } + 4000$ , where x is time in years since 2010. By sketching a graph of P(x), estimate during what time period the population of the city would be increasing.

Find all rational zeros of the polynomial function. - $f ( x ) = 4 x ^ { 3 } + 13 x ^ { 2 } - 37 x - 10$

$x ^ { 4 } - 81 = 0$

Use analytical methods to solve the equation. - $\frac { 8 } { x + 6 } = - \frac { 7 } { 9 }$

Use the given graph of the polynomial function to state whether the leading coefficient is positive or negative and whether the polynomial function is cubic or quartic. -

$\frac { 3 x + 6 } { 5 x ^ { 2 } + 5 } > 0$

Use a graphing calculator to estimate the local maximum and local minimum values of the function to the nearest hundredth. - $y = 3 x ^ { 3 } - 4 x ^ { 2 } - 6 x + 2$

Use the given graph of the polynomial function to state whether the leading coefficient is positive or negative and whether the polynomial function is cubic or quartic. -

Determine all possible rational solutions of the polynomial equation. - $f ( x ) = - 2 x ^ { 4 } + 4 x ^ { 3 } + 5 x ^ { 2 } + 18$

Use the graph of the polynomial function f(x) to solve f( $f ( x ) \text { to solve } f ( x ) = 0$ - $Use the graph of the polynomial function f(x) to solve f( f ( x ) \text { to solve } f ( x ) = 0 -$

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

Choose the graph that satisfies the given conditions. -Polynomial of degree 3 with three distinct x $\text { x-intercepts a }$ nd a positive leading coefficient

An architect needs to design a rectangular room with an area of 97 ft² . What dimensions should he use in order to minimize the perimeter?

Find the cubic or quartic function that models the data in the table. - x -5 0 2 3 y -60 5 3 10 start text left parenthesisCubicright parenthesis end text

Determine whether the given constant is a solution to the given polynomial equation. - $- 9 x ^ { 3 } + x ^ { 2 } - 3 x + 6 = 0 ; - 1$

Use graphical methods to find any turning points of the graph of the function. - $f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 3 }$

Solve the equation exactly in the complex number system. - $x ^ { 3 } + 4 x ^ { 2 } - 2 x - 8 = 0$

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

Match the function with its graph. - f(x)=x−4x+5f ( x ) = \frac { x - 4 } { x + 5 }f(x)=x+5x−4​

Predict the end behavior of the graph of the function. - f(x)=3.63x4+6x2+x−2f ( x ) = 3.63 x ^ { 4 } + 6 x ^ { 2 } + x - 2f(x)=3.63x4+6x2+x−2

Find all rational zeros of the polynomial function. - f(x)=4x3+13x2−37x−10f ( x ) = 4 x ^ { 3 } + 13 x ^ { 2 } - 37 x - 10f(x)=4x3+13x2−37x−10

x4−81=0x ^ { 4 } - 81 = 0x4−81=0

Use analytical methods to solve the equation. - 8x+6=−79\frac { 8 } { x + 6 } = - \frac { 7 } { 9 }x+68​=−97​

Use the given graph of the polynomial function to state whether the leading coefficient is positive or negative and whether the polynomial function is cubic or quartic. -

3x+65x2+5>0\frac { 3 x + 6 } { 5 x ^ { 2 } + 5 } > 05x2+53x+6​>0

Use a graphing calculator to estimate the local maximum and local minimum values of the function to the nearest hundredth. - y=3x3−4x2−6x+2y = 3 x ^ { 3 } - 4 x ^ { 2 } - 6 x + 2y=3x3−4x2−6x+2

Use the given graph of the polynomial function to state whether the leading coefficient is positive or negative and whether the polynomial function is cubic or quartic. -

Determine all possible rational solutions of the polynomial equation. - f(x)=−2x4+4x3+5x2+18f ( x ) = - 2 x ^ { 4 } + 4 x ^ { 3 } + 5 x ^ { 2 } + 18f(x)=−2x4+4x3+5x2+18

Use the graph of the polynomial function f(x) to solve f( f(x) to solve f(x)=0f ( x ) \text { to solve } f ( x ) = 0f(x) to solve f(x)=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​

Choose the graph that satisfies the given conditions. -Polynomial of degree 3 with three distinct x x-intercepts a \text { x-intercepts a } x-intercepts a nd a positive leading coefficient

An architect needs to design a rectangular room with an area of 97 ft2 . What dimensions should he use in order to minimize the perimeter?

Find the cubic or quartic function that models the data in the table. - x -5 0 2 3 y -60 5 3 10 start text left parenthesisCubicright parenthesis end text

Determine whether the given constant is a solution to the given polynomial equation. - −9x3+x2−3x+6=0;−1- 9 x ^ { 3 } + x ^ { 2 } - 3 x + 6 = 0 ; - 1−9x3+x2−3x+6=0;−1

Use graphical methods to find any turning points of the graph of the function. - f(x)=x2x2+3f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 3 }f(x)=x2+3x2​

Solve the equation exactly in the complex number system. - x3+4x2−2x−8=0x ^ { 3 } + 4 x ^ { 2 } - 2 x - 8 = 0x3+4x2−2x−8=0

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

Match the function with its graph. - $f ( x ) = \frac { x - 4 } { x + 5 }$

Predict the end behavior of the graph of the function. - $f ( x ) = 3.63 x ^ { 4 } + 6 x ^ { 2 } + x - 2$

Find all rational zeros of the polynomial function. - $f ( x ) = 4 x ^ { 3 } + 13 x ^ { 2 } - 37 x - 10$

$x ^ { 4 } - 81 = 0$

Use analytical methods to solve the equation. - $\frac { 8 } { x + 6 } = - \frac { 7 } { 9 }$

$\frac { 3 x + 6 } { 5 x ^ { 2 } + 5 } > 0$

Use a graphing calculator to estimate the local maximum and local minimum values of the function to the nearest hundredth. - $y = 3 x ^ { 3 } - 4 x ^ { 2 } - 6 x + 2$

Determine all possible rational solutions of the polynomial equation. - $f ( x ) = - 2 x ^ { 4 } + 4 x ^ { 3 } + 5 x ^ { 2 } + 18$

Use the graph of the polynomial function f(x) to solve f( $f ( x ) \text { to solve } f ( x ) = 0$ - $Use the graph of the polynomial function f(x) to solve f( f ( x ) \text { to solve } f ( x ) = 0 -$

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

Choose the graph that satisfies the given conditions. -Polynomial of degree 3 with three distinct x $\text { x-intercepts a }$ nd a positive leading coefficient

An architect needs to design a rectangular room with an area of 97 ft² . What dimensions should he use in order to minimize the perimeter?

Determine whether the given constant is a solution to the given polynomial equation. - $- 9 x ^ { 3 } + x ^ { 2 } - 3 x + 6 = 0 ; - 1$

Use graphical methods to find any turning points of the graph of the function. - $f ( x ) = \frac { x ^ { 2 } } { x ^ { 2 } + 3 }$

Solve the equation exactly in the complex number system. - $x ^ { 3 } + 4 x ^ { 2 } - 2 x - 8 = 0$