Question 1

Write an equation for the quadratic function whose graph contains the given vertex and point.
-Vertex $( 2 , - 5 )$, point $( - 4 , - 41 )$

Accepted Answer

A)  $P ( x ) = x ^ { 2 } - 4 x - 5$ 
B)  $P ( x ) = - 4 x ^ { 2 } - 4 x + 9$ 
C)  $P ( x ) = - x ^ { 2 } + 4 x - 9$ 
D)  $P ( x ) = - x ^ { 2 } - 2 x - 5$ 
A)  $P ( x ) = x ^ { 2 } - 4 x - 5$ 
B)  $P ( x ) = - 4 x ^ { 2 } - 4 x + 9$ 
C)  $P ( x ) = - x ^ { 2 } + 4 x - 9$ 
D)  $P ( x ) = - x ^ { 2 } - 2 x - 5$

Question 2

Write the word or phrase that best completes each statement or answers the question.
Graph the rational function and analyze it in the following way: find the intercepts, asymptotes, use limits to describe the
behavior at the vertical asymptotes and the end behavior. Find the domain and range. Determine where the function is
continuous and where it is increasing and decreasing. Find any local extrema.
-$$f ( x ) = \frac { x ^ { 2 } + x - 2 } { x ^ { 2 } - 3 x - 4 }$$

Accepted Answer

@#LAT-DLM&-intercepts: @#LAT-DLM& and @#LAT-DLM&
@#LAT-DLM&-intercept:

Question 3

Determine the x values that cause the function to be (a) zero, (b) undefined, (c) positive, and (d) negative.
-$$f ( x ) = \frac { 3 x - 4 } { ( x + 6 ) \sqrt { x - 5 } }$$

Accepted Answer

A)  (a) $\varnothing$, (b) $(\infty , 5 )$, (c) $\varnothing$, (d) $( 5 , \infty )$ 
B)  (a) $\left\{ \frac { 4 } { 3 } \right\} \left( \right.$ b) $\{ - 6,5 \}$, (c) $\left( - 6 , \frac { 4 } { 3 } \right) \cup \left( \frac { 5 } { 3 } , \infty \right)$, (d) $(\infty , - 6 ) \cup \left( \frac { 4 } { 3 } , 5 \right)$ 
C)  (a) $\varnothing$, (b) $( - 5,5 )$, (c) $( 5 , \infty )$, (d) $\varnothing$ 
D)  (a) $\left\{ \frac { 4 } { 3 } \right\}$ (b) $\{ - 6,5 \} , \left( \right.$ c) $( - , - 6 ) \cup \left( \frac { 4 } { 3 } , 5 \right)$, (d) $\left( - 6 , \frac { 4 } { 3 } \right) \cup \left( \frac { 5 } { 3 } , \infty \right)$ 
A)  (a) $\varnothing$, (b) $(\infty , 5 )$, (c) $\varnothing$, (d) $( 5 , \infty )$ 
B)  (a) $\left\{ \frac { 4 } { 3 } \right\} \left( \right.$ b) $\{ - 6,5 \}$, (c) $\left( - 6 , \frac { 4 } { 3 } \right) \cup \left( \frac { 5 } { 3 } , \infty \right)$, (d) $(\infty , - 6 ) \cup \left( \frac { 4 } { 3 } , 5 \right)$ 
C)  (a) $\varnothing$, (b) $( - 5,5 )$, (c) $( 5 , \infty )$, (d) $\varnothing$ 
D)  (a) $\left\{ \frac { 4 } { 3 } \right\}$ (b) $\{ - 6,5 \} , \left( \right.$ c) $( - , - 6 ) \cup \left( \frac { 4 } { 3 } , 5 \right)$, (d) $\left( - 6 , \frac { 4 } { 3 } \right) \cup \left( \frac { 5 } { 3 } , \infty \right)$

Question 4

Use a cubic or quartic regression (as specified) to fit a curve through the points given in the table. Round to the nearest
hundredth.
-

Accepted Answer

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

Question 5

Describe how the graph of the given function can be obtained by transforming the graph of the reciprocal function f(x) =
1/x.
-$$f ( x ) = \frac { 2 - 3 x } { x - 4 }$$

Accepted Answer

A)  Shift the graph of the reciprocal function right 4 units, stretch vertically by a factor of 10 , and then shift 3 units down. 
B)  Shift the graph of the reciprocal function right 4 units, reflect across the $x$-axis, stretch vertically by a factor of 10, and then shift 3 units down. 
C)  Shift the graph of the reciprocal function right 4 units, reflect across the x-axis, stretch vertically by a factor of 10, and then shift 3 units up. 
D)  Shift the graph of the reciprocal function right 4 units, stretch vertically by a factor of 10 , and then shift 3 units up. 
A)  Shift the graph of the reciprocal function right 4 units, stretch vertically by a factor of 10 , and then shift 3 units down. 
B)  Shift the graph of the reciprocal function right 4 units, reflect across the $x$-axis, stretch vertically by a factor of 10, and then shift 3 units down. 
C)  Shift the graph of the reciprocal function right 4 units, reflect across the x-axis, stretch vertically by a factor of 10, and then shift 3 units up. 
D)  Shift the graph of the reciprocal function right 4 units, stretch vertically by a factor of 10 , and then shift 3 units up.

Question 6

Write an equation for the quadratic function whose graph contains the given vertex and point.
-Vertex $( - 3,5 )$, point $( 3,113 )$

Accepted Answer

A)  $P ( x ) = 3 x ^ { 2 } + 3 x + 5$ 
B)  $P ( x ) = - 3 x ^ { 2 } + 18 x + 5$ 
C)  $P ( x ) = 3 x ^ { 2 } - 18 x + 32$ 
D)  $P ( x ) = 3 x ^ { 2 } + 18 x + 32$ 
A)  $P ( x ) = 3 x ^ { 2 } + 3 x + 5$ 
B)  $P ( x ) = - 3 x ^ { 2 } + 18 x + 5$ 
C)  $P ( x ) = 3 x ^ { 2 } - 18 x + 32$ 
D)  $P ( x ) = 3 x ^ { 2 } + 18 x + 32$

Question 7

Solve the problem. Round as appropriate.
-The volume $\mathrm { V }$ of a given mass of gas varies directly as the temperature $\mathrm { T }$ and inversely as the pressure $\mathrm { P }$. If $\mathrm { V } =$ $286.0 \mathrm { in } ^ { 3 }$ when $\mathrm { T } = 260 ^ { \circ }$ and $\mathrm { P } = 10 \mathrm { lb } / \mathrm { in } ^ { 2 }$, what is the volume when $\mathrm { T } = 260 ^ { \circ }$ and $\mathrm { P } = 20 \mathrm { lb } / \mathrm { in } ^ { 2 }$ ?

Accepted Answer

A)  $183.0 \mathrm { in } ^ { 3 }$ 
B)  $133.0 \mathrm { in } ^ { 3 }$ 
C)  $143.0 \mathrm { in } ^ { 3 }$ 
D)  $123.0 \mathrm { in } ^ { 3 }$ 
A)  $183.0 \mathrm { in } ^ { 3 }$ 
B)  $133.0 \mathrm { in } ^ { 3 }$ 
C)  $143.0 \mathrm { in } ^ { 3 }$ 
D)  $123.0 \mathrm { in } ^ { 3 }$

Question 8

Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or irrational.
-$$f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 7 x + 21$$

Accepted Answer

A)  3 (rational), 7 (rational), and $- 7$ (rational) 
B)  3 (rational), $2 \sqrt { 7 }$ (irrational), and $- 2 \sqrt { 7 }$ (irrational) 
C)  3 (rational), $\sqrt { 7 }$ (irrational), and $- \sqrt { 7 }$ (irrational) 
D)  $- 3$ (rational), $\sqrt { 7 }$ (irrational), and $- \sqrt { 7 }$ (irrational) 
A)  3 (rational), 7 (rational), and $- 7$ (rational) 
B)  3 (rational), $2 \sqrt { 7 }$ (irrational), and $- 2 \sqrt { 7 }$ (irrational) 
C)  3 (rational), $\sqrt { 7 }$ (irrational), and $- \sqrt { 7 }$ (irrational) 
D)  $- 3$ (rational), $\sqrt { 7 }$ (irrational), and $- \sqrt { 7 }$ (irrational)

Question 9

Determine whether the power function is even, odd, or neither.
-$$f ( x ) = \frac { 2 }{ 11 } x^{ 11 / 2}$$

Accepted Answer

A)  Odd 
B)  Neither 
C)  Even 
A)  Odd 
B)  Neither 
C)  Even

Question 10

Graph the function in a viewing window that shows all of its extrema and x-intercepts.
-$$f ( x ) = - x ^ { 3 } - 5 x ^ { 2 } - 19 x + 30$$

Accepted Answer

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

Question 11

Divide using synthetic division, and write a summary statement in fraction form.
-$\frac { - 5 x ^ { 4 } + x ^ { 3 } + 2 x ^ { 2 } + 3 x - 1 } { x - 1 }$

Accepted Answer

A)  $- 5 x ^ { 3 } + 4 x ^ { 2 } - 2 x - 1$ 
B)  $- 5 x ^ { 3 } + 4 x ^ { 2 } + 6 x + 9$ 
C)  $- 5 x ^ { 3 } - 4 x ^ { 2 } - 2 x + 1$ 
D)  $- 5 x ^ { 3 } + 6 x ^ { 2 } - 4 x - 1$ 
A)  $- 5 x ^ { 3 } + 4 x ^ { 2 } - 2 x - 1$ 
B)  $- 5 x ^ { 3 } + 4 x ^ { 2 } + 6 x + 9$ 
C)  $- 5 x ^ { 3 } - 4 x ^ { 2 } - 2 x + 1$ 
D)  $- 5 x ^ { 3 } + 6 x ^ { 2 } - 4 x - 1$

Question 12

State the domain of the rational function.
-$$f ( x ) = \frac { 14 } { x + 5 }$$

Accepted Answer

A)  $( - \infty , \infty )$ 
B)  $( - \infty , 5 ) \cup ( 5 , \infty )$ 
C)  $( - 5 , \infty )$ 
D)  $( - \infty , - 5 ) \cup ( - 5 , \infty )$ 
A)  $( - \infty , \infty )$ 
B)  $( - \infty , 5 ) \cup ( 5 , \infty )$ 
C)  $( - 5 , \infty )$ 
D)  $( - \infty , - 5 ) \cup ( - 5 , \infty )$

Question 13

Choose the one alternative that best completes the statement or answers the question.
Describe how to obtain the graph of the given monomial function from the graph of g(x) = xn with the same power n.
-$$f ( x ) = \frac { 1 } { 4 } x ^ { 4 }$$

Accepted Answer

A)  Vertically shrink by a factor of $\frac { 1 } { 4 }$ 
B)  Vertically shrink by a factor of $\frac { 1 } { 4 }$, and then reflect across $x$-axis 
C)  Vertically stretch by a factor of 4 , and then reflect across $x$-axis 
D)  Horizontally shrink by a factor of $\frac { 1 } { 4 }$ 
A)  Vertically shrink by a factor of $\frac { 1 } { 4 }$ 
B)  Vertically shrink by a factor of $\frac { 1 } { 4 }$, and then reflect across $x$-axis 
C)  Vertically stretch by a factor of 4 , and then reflect across $x$-axis 
D)  Horizontally shrink by a factor of $\frac { 1 } { 4 }$

Question 14

Solve the polynomial inequality.
-$$( x + 1 ) ( x - 6 ) ( x - 7 ) > 0$$

Accepted Answer

A)  $( - \infty , 6 )$ 
B)  $( - \infty , - 1 ) \cup ( 6,7 )$ 
C)  $( - 1,6 ) \cup ( 7 , \infty )$ 
D)  $( 7 , \infty )$ 
A)  $( - \infty , 6 )$ 
B)  $( - \infty , - 1 ) \cup ( 6,7 )$ 
C)  $( - 1,6 ) \cup ( 7 , \infty )$ 
D)  $( 7 , \infty )$

Question 15

Write the word or phrase that best completes each statement or answers the question.
Write a sentence that expresses the relationship in the formula, using the language of variation or proportion.
-$$r = \frac { d } { t } \text {, where } r \text { is the rate by which distance } d \text { is covered in time } t$$

Accepted Answer

Rate is directly pro

Question 16

Solve the problem.
-A rectangular piece of cardboard measuring 24 inches by 30 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)  $121.87$ 
B)  $585.52$ 
C)  $1417.87$ 
D)  $20,046.4$ 
A)  $121.87$ 
B)  $585.52$ 
C)  $1417.87$ 
D)  $20,046.4$

Question 17

Write the function as a product of linear and irreducible quadratic factors, all with real coefficients.
-$$f ( x ) = x ^ { 4 } - 4 x ^ { 3 } - 11 x ^ { 2 } - 4 x - 12$$

Accepted Answer

A)  $( x - 6 ) ( x - 2 ) \left( x ^ { 2 } + 1 \right)$ 
B)  $( x - 6 ) ( x + 2 ) \left( x ^ { 2 } + 1 \right)$ 
C)  $( x + 6 ) ( x + 2 ) \left( x ^ { 2 } + 1 \right)$ 
D)  $( x - 6 ) ^ { 2 } \left( x ^ { 2 } + 1 \right)$ 
A)  $( x - 6 ) ( x - 2 ) \left( x ^ { 2 } + 1 \right)$ 
B)  $( x - 6 ) ( x + 2 ) \left( x ^ { 2 } + 1 \right)$ 
C)  $( x + 6 ) ( x + 2 ) \left( x ^ { 2 } + 1 \right)$ 
D)  $( x - 6 ) ^ { 2 } \left( x ^ { 2 } + 1 \right)$

Question 18

Graph the function in a viewing window that shows all of its extrema and x-intercepts.
-$$f ( x ) = 2 x ( x + 1 ) ( x + 2 )$$

Accepted Answer

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

Question 19

Use a cubic or quartic regression (as specified) to fit a curve through the points given in the table. Round to the nearest
hundredth.
-

Accepted Answer

A)  $y \approx 0.28 x ^ { 3 } - 5.35 x ^ { 2 } + 22.97 x - 33.40$ 
B)  $y \approx 0.28 x ^ { 3 } - 4.35 x ^ { 2 } + 24.97 x - 33.40$ 
C)  $y \approx 0.38 x ^ { 3 } - 5.35 x ^ { 2 } + 24.97 x - 33.40$ 
D)  $y \approx 0.38 x ^ { 3 } - 4.35 x ^ { 2 } + 22.97 x - 33.40$ 
A)  $y \approx 0.28 x ^ { 3 } - 5.35 x ^ { 2 } + 22.97 x - 33.40$ 
B)  $y \approx 0.28 x ^ { 3 } - 4.35 x ^ { 2 } + 24.97 x - 33.40$ 
C)  $y \approx 0.38 x ^ { 3 } - 5.35 x ^ { 2 } + 24.97 x - 33.40$ 
D)  $y \approx 0.38 x ^ { 3 } - 4.35 x ^ { 2 } + 22.97 x - 33.40$

Question 20

Use the graph to guess possible linear factors of f(x). Then completely factor f(x) with the aid of synthetic division.
-$f(x)=5 x^{3}+33 x^{2}+31 x-69$

Accepted Answer

A)  $f ( x ) = ( x + 3 ) ( 5 x + 23 ) ( x - 1 )$ 
B)  $f ( x ) = ( x + 3 ) ( 7 x + 31 ) ( x - 1 )$ 
C)  $f ( x ) = ( x - 3 ) ( 5 x - 23 ) ( x + 1 )$ 
D)  $f ( x ) = ( x - 3 ) ( 5 x - 21 ) ( x + 1 )$ 
A)  $f ( x ) = ( x + 3 ) ( 5 x + 23 ) ( x - 1 )$ 
B)  $f ( x ) = ( x + 3 ) ( 7 x + 31 ) ( x - 1 )$ 
C)  $f ( x ) = ( x - 3 ) ( 5 x - 23 ) ( x + 1 )$ 
D)  $f ( x ) = ( x - 3 ) ( 5 x - 21 ) ( x + 1 )$

Write an equation for the quadratic function whose graph contains the given vertex and point. -Vertex $( 2 , - 5 )$ , point $( - 4 , - 41 )$

Determine the x values that cause the function to be (a) zero, (b) undefined, (c) positive, and (d) negative. - $f ( x ) = \frac { 3 x - 4 } { ( x + 6 ) \sqrt { x - 5 } }$

Use a cubic or quartic regression (as specified) to fit a curve through the points given in the table. Round to the nearest hundredth. -

Describe how the graph of the given function can be obtained by transforming the graph of the reciprocal function f(x) = 1/x. - $f ( x ) = \frac { 2 - 3 x } { x - 4 }$

Write an equation for the quadratic function whose graph contains the given vertex and point. -Vertex $( - 3,5 )$ , point $( 3,113 )$

Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or irrational. - $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 7 x + 21$

Determine whether the power function is even, odd, or neither. - $f ( x ) = \frac { 2 }{ 11 } x^{ 11 / 2}$

Graph the function in a viewing window that shows all of its extrema and x-intercepts. - $f ( x ) = - x ^ { 3 } - 5 x ^ { 2 } - 19 x + 30$ $Graph the function in a viewing window that shows all of its extrema and x-intercepts. - f ( x ) = - x ^ { 3 } - 5 x ^ { 2 } - 19 x + 30$

Divide using synthetic division, and write a summary statement in fraction form. - $\frac { - 5 x ^ { 4 } + x ^ { 3 } + 2 x ^ { 2 } + 3 x - 1 } { x - 1 }$

State the domain of the rational function. - $f ( x ) = \frac { 14 } { x + 5 }$

Choose the one alternative that best completes the statement or answers the question. Describe how to obtain the graph of the given monomial function from the graph of g(x) = xn with the same power n. - $f ( x ) = \frac { 1 } { 4 } x ^ { 4 }$

Solve the polynomial inequality. - $( x + 1 ) ( x - 6 ) ( x - 7 ) > 0$

Write the function as a product of linear and irreducible quadratic factors, all with real coefficients. - $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } - 11 x ^ { 2 } - 4 x - 12$

Graph the function in a viewing window that shows all of its extrema and x-intercepts. - $f ( x ) = 2 x ( x + 1 ) ( x + 2 )$

Use a cubic or quartic regression (as specified) to fit a curve through the points given in the table. Round to the nearest hundredth. -

Functions and Graphs

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An Introduction to Calculus: Limits, Derivatives, and Integrals

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Exam 2: Polynomial, Power, and Rational Functions

Write an equation for the quadratic function whose graph contains the given vertex and point. -Vertex (2,−5)( 2 , - 5 )(2,−5) , point (−4,−41)( - 4 , - 41 )(−4,−41)

Determine the x values that cause the function to be (a) zero, (b) undefined, (c) positive, and (d) negative. - f(x)=3x−4(x+6)x−5f ( x ) = \frac { 3 x - 4 } { ( x + 6 ) \sqrt { x - 5 } }f(x)=(x+6)x−5​3x−4​

Use a cubic or quartic regression (as specified) to fit a curve through the points given in the table. Round to the nearest hundredth. -

Describe how the graph of the given function can be obtained by transforming the graph of the reciprocal function f(x) = 1/x. - f(x)=2−3xx−4f ( x ) = \frac { 2 - 3 x } { x - 4 }f(x)=x−42−3x​

Write an equation for the quadratic function whose graph contains the given vertex and point. -Vertex (−3,5)( - 3,5 )(−3,5) , point (3,113)( 3,113 )(3,113)

Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or irrational. - f(x)=x3−3x2−7x+21f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 7 x + 21f(x)=x3−3x2−7x+21

Determine whether the power function is even, odd, or neither. - f(x)=211x11/2f ( x ) = \frac { 2 }{ 11 } x^{ 11 / 2}f(x)=112​x11/2

Graph the function in a viewing window that shows all of its extrema and x-intercepts. - f(x)=−x3−5x2−19x+30f ( x ) = - x ^ { 3 } - 5 x ^ { 2 } - 19 x + 30f(x)=−x3−5x2−19x+30

Divide using synthetic division, and write a summary statement in fraction form. - −5x4+x3+2x2+3x−1x−1\frac { - 5 x ^ { 4 } + x ^ { 3 } + 2 x ^ { 2 } + 3 x - 1 } { x - 1 }x−1−5x4+x3+2x2+3x−1​

State the domain of the rational function. - f(x)=14x+5f ( x ) = \frac { 14 } { x + 5 }f(x)=x+514​

Choose the one alternative that best completes the statement or answers the question. Describe how to obtain the graph of the given monomial function from the graph of g(x) = xn with the same power n. - f(x)=14x4f ( x ) = \frac { 1 } { 4 } x ^ { 4 }f(x)=41​x4

Solve the polynomial inequality. - (x+1)(x−6)(x−7)>0( x + 1 ) ( x - 6 ) ( x - 7 ) > 0(x+1)(x−6)(x−7)>0

Write the function as a product of linear and irreducible quadratic factors, all with real coefficients. - f(x)=x4−4x3−11x2−4x−12f ( x ) = x ^ { 4 } - 4 x ^ { 3 } - 11 x ^ { 2 } - 4 x - 12f(x)=x4−4x3−11x2−4x−12

Graph the function in a viewing window that shows all of its extrema and x-intercepts. - f(x)=2x(x+1)(x+2)f ( x ) = 2 x ( x + 1 ) ( x + 2 )f(x)=2x(x+1)(x+2)

Use a cubic or quartic regression (as specified) to fit a curve through the points given in the table. Round to the nearest hundredth. -

Use the graph to guess possible linear factors of f(x). Then completely factor f(x) with the aid of synthetic division. - f(x)=5x3+33x2+31x−69f(x)=5 x^{3}+33 x^{2}+31 x-69f(x)=5x3+33x2+31x−69

Functions and Graphs

Exponential, Logistic, and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometry

Systems and Matrices

Analytic Geometry in Two and Three Dimensions

Discrete Mathematics

Statistics and Probability

An Introduction to Calculus: Limits, Derivatives, and Integrals

Prerequisites

Filters

Write an equation for the quadratic function whose graph contains the given vertex and point. -Vertex $( 2 , - 5 )$ , point $( - 4 , - 41 )$

Determine the x values that cause the function to be (a) zero, (b) undefined, (c) positive, and (d) negative. - $f ( x ) = \frac { 3 x - 4 } { ( x + 6 ) \sqrt { x - 5 } }$

Describe how the graph of the given function can be obtained by transforming the graph of the reciprocal function f(x) = 1/x. - $f ( x ) = \frac { 2 - 3 x } { x - 4 }$

Write an equation for the quadratic function whose graph contains the given vertex and point. -Vertex $( - 3,5 )$ , point $( 3,113 )$

Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or irrational. - $f ( x ) = x ^ { 3 } - 3 x ^ { 2 } - 7 x + 21$

Determine whether the power function is even, odd, or neither. - $f ( x ) = \frac { 2 }{ 11 } x^{ 11 / 2}$

Graph the function in a viewing window that shows all of its extrema and x-intercepts. - $f ( x ) = - x ^ { 3 } - 5 x ^ { 2 } - 19 x + 30$ $Graph the function in a viewing window that shows all of its extrema and x-intercepts. - f ( x ) = - x ^ { 3 } - 5 x ^ { 2 } - 19 x + 30$

Divide using synthetic division, and write a summary statement in fraction form. - $\frac { - 5 x ^ { 4 } + x ^ { 3 } + 2 x ^ { 2 } + 3 x - 1 } { x - 1 }$

State the domain of the rational function. - $f ( x ) = \frac { 14 } { x + 5 }$

Choose the one alternative that best completes the statement or answers the question. Describe how to obtain the graph of the given monomial function from the graph of g(x) = xn with the same power n. - $f ( x ) = \frac { 1 } { 4 } x ^ { 4 }$

Solve the polynomial inequality. - $( x + 1 ) ( x - 6 ) ( x - 7 ) > 0$

Write the function as a product of linear and irreducible quadratic factors, all with real coefficients. - $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } - 11 x ^ { 2 } - 4 x - 12$

Graph the function in a viewing window that shows all of its extrema and x-intercepts. - $f ( x ) = 2 x ( x + 1 ) ( x + 2 )$