Question 1

Use the Rational Zeros Theorem to write a list of all potential rational zeros
-$$f ( x ) = - 2 x ^ { 4 } + 5 x ^ { 3 } + 6 x ^ { 2 } + 18$$

Accepted Answer

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

Question 2

For the given function, find all asymptotes of the type indicated (if there are any)
-$f ( x ) = \frac { x - 9 } { x ^ { 2 } - 25 }$, vertical

Accepted Answer

A)  $x = 5 , x = - 5$ 
B)  $x = 5$ 
C)  $x = - 5$ 
D)  $x = 9$ 
A)  $x = 5 , x = - 5$ 
B)  $x = 5$ 
C)  $x = - 5$ 
D)  $x = 9$

Question 3

Match the polynomial function graph to the appropriate zeros and multiplicities.
-

Accepted Answer

A)  $- 3$ (multiplicity 4), 2 (multiplicity 4) 
B)  $- 3$ (multiplicity 4), 2 (multiplicity 3) 
C)  2 (multiplicity 4), $- 3$ (multiplicity 3) 
D)  2 (multiplicity 3 ), $- 3$ (multiplicity 2) 
A)  $- 3$ (multiplicity 4), 2 (multiplicity 4) 
B)  $- 3$ (multiplicity 4), 2 (multiplicity 3) 
C)  2 (multiplicity 4), $- 3$ (multiplicity 3) 
D)  2 (multiplicity 3 ), $- 3$ (multiplicity 2)

Question 4

Solve the problem.
-The table shows the population of a certain city in various different years. Use regression to find values for a and $b$ so that $f ( x ) = a x ^ { b }$ models this data, where $x$ represents the number of years since 1980 and $f ( x )$ is the population of the city in hundreds of thousands. Round your answers to 4 decimal places.

Accepted Answer

A)  $a \approx 1.7025 , b \approx 0.5375$ 
B)  $\mathrm { a } \approx 2.1375 , \mathrm {~b} \approx 0.4432$ 
C)  $a \approx 2.6352 , b \approx 0.4756$ 
D)  $\mathrm { a } \approx 1.8506 , \mathrm {~b} \approx 0.5121$ 
A)  $a \approx 1.7025 , b \approx 0.5375$ 
B)  $\mathrm { a } \approx 2.1375 , \mathrm {~b} \approx 0.4432$ 
C)  $a \approx 2.6352 , b \approx 0.4756$ 
D)  $\mathrm { a } \approx 1.8506 , \mathrm {~b} \approx 0.5121$

Question 5

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the
polynomial in standard form.
-$5 i$ and $\sqrt { 2 }$

Accepted Answer

A)  $f ( x ) = x ^ { 4 } - 23 x ^ { 2 } - 50$ 
B)  $f ( x ) = x ^ { 4 } + 23 x ^ { 2 } - 50$ 
C)  $f ( x ) = x ^ { 4 } - 46 x ^ { 2 } + 50$ 
D)  $f ( x ) = x ^ { 4 } + 46 x ^ { 2 } + 50$ 
A)  $f ( x ) = x ^ { 4 } - 23 x ^ { 2 } - 50$ 
B)  $f ( x ) = x ^ { 4 } + 23 x ^ { 2 } - 50$ 
C)  $f ( x ) = x ^ { 4 } - 46 x ^ { 2 } + 50$ 
D)  $f ( x ) = x ^ { 4 } + 46 x ^ { 2 } + 50$

Question 6

Solve the problem.
-The first column shows the independent variable (x). The second column shows the dependent variable (y).

Find the linear regression model.

Accepted Answer

A)  $y = 3.84 x + 7.94$ 
B)  $y = 2.84 x + 6.94$ 
C)  $y = 2.34 x + 6.44$ 
D)  $y = 3.34 x + 6.44$ 
A)  $y = 3.84 x + 7.94$ 
B)  $y = 2.84 x + 6.94$ 
C)  $y = 2.34 x + 6.44$ 
D)  $y = 3.34 x + 6.44$

Question 7

Use limits to describe the behavior of the rational function near the indicated asymptote.
-$$f ( x ) = \frac { 1 - 5 x } { x + 2 }$$
Describe the behavior of the function near its horizontal asymptote (the end behavior).

Accepted Answer

A)  $\lim _ { x \rightarrow \infty } f ( x ) = 0 , \quad \lim _ { x \rightarrow \infty } f ( x ) = 0$ 
B)  $\lim _ { x \rightarrow \infty } f ( x ) = - 5 , \lim _ { x \rightarrow \infty } f ( x ) = - 5$ 
C) 
  
D)  $\lim _ { x \rightarrow \infty } f ( x ) = 5 , \lim _ { x \rightarrow \infty } f ( x ) = - 5$ 
A)  $\lim _ { x \rightarrow \infty } f ( x ) = 0 , \quad \lim _ { x \rightarrow \infty } f ( x ) = 0$ 
B)  $\lim _ { x \rightarrow \infty } f ( x ) = - 5 , \lim _ { x \rightarrow \infty } f ( x ) = - 5$ 
C) 
  
D)  $\lim _ { x \rightarrow \infty } f ( x ) = 5 , \lim _ { x \rightarrow \infty } f ( x ) = - 5$

Question 8

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.
-$$f ( x ) = \frac { 1 } { 2 } x ^ { 7 }$$

Accepted Answer

A)  Vertically shrink by a factor of $\frac { 1 } { 2 }$, and then reflect across $x$-axis 
B)  Vertically shrink by a factor of $\frac { 1 } { 2 }$ 
C)  Vertically stretch by a factor of 2 
D)  Horizontally shrink by a factor of $\frac { 1 } { 2 }$ 
A)  Vertically shrink by a factor of $\frac { 1 } { 2 }$, and then reflect across $x$-axis 
B)  Vertically shrink by a factor of $\frac { 1 } { 2 }$ 
C)  Vertically stretch by a factor of 2 
D)  Horizontally shrink by a factor of $\frac { 1 } { 2 }$

Question 9

Determine the x values that cause the polynomial function to be (a) zero, (b) positive, and (c) negative.
-$$f ( x ) = ( x + 2 ) ( x + 1 ) ( x - 2 )$$

Accepted Answer

A)  (a) $\{ 2,1 , - 2 \}$, (b) $( - 2 , - 1 ) \cup ( 2 , \infty )$, (c) $( * , - 2 ) \cup ( - 1,2 )$ 
B)  (a) $\{ - 2 , - 1,2 \}$, (b) $( - 2 , - 1 ) \cup ( 2 , \infty )$, (c) $( \infty , - 2 ) \cup ( - 1,2 )$ 
C)  (a) $\{ - 2 , - 1,2 \}$, (b) $( \infty , - 2 ) \cup ( - 1,2 \}$, (c) $( - 2 , - 1 ) \cup ( 2 , \infty )$ 
D)  (a) $\{ - 2 , - 1,2 \}$, (b) $( - 2,2 )$, (c) $( \infty , - 2 ) \cup ( 2 , \infty )$ 
A)  (a) $\{ 2,1 , - 2 \}$, (b) $( - 2 , - 1 ) \cup ( 2 , \infty )$, (c) $( * , - 2 ) \cup ( - 1,2 )$ 
B)  (a) $\{ - 2 , - 1,2 \}$, (b) $( - 2 , - 1 ) \cup ( 2 , \infty )$, (c) $( \infty , - 2 ) \cup ( - 1,2 )$ 
C)  (a) $\{ - 2 , - 1,2 \}$, (b) $( \infty , - 2 ) \cup ( - 1,2 \}$, (c) $( - 2 , - 1 ) \cup ( 2 , \infty )$ 
D)  (a) $\{ - 2 , - 1,2 \}$, (b) $( - 2,2 )$, (c) $( \infty , - 2 ) \cup ( 2 , \infty )$

Question 10

Solve the problem. Round as appropriate.
-The time T necessary to make an enlargement of a photo negative varies directly as the area A of the enlargement. If 60 seconds are required to make a 3-by-5 enlargement, find the time required for a 5-by-6
Enlargement.

Accepted Answer

A)  150 sec 
B)  90 sec 
C)  120 sec 
D)  180 sec 
A)  150 sec 
B)  90 sec 
C)  120 sec 
D)  180 sec

Question 11

Describe the strength and direction of the linear correlation.
-

Accepted Answer

A)  Weak positive linear correlation 
B)  Weak negative linear correlation 
C)  Strong negative linear correlation 
D)  Little or no linear correlation 
A)  Weak positive linear correlation 
B)  Weak negative linear correlation 
C)  Strong negative linear correlation 
D)  Little or no linear correlation

Question 12

Find the axis of the graph of the function.
-$$f ( x ) = 4 ( x - \sqrt { 7 } ) ^ { 2 } + 5$$

Accepted Answer

A)  $x = - 7$ 
B)  $x = 7$ 
C)  $x = \sqrt { 7 }$ 
D)  $x = - \sqrt { 7 }$ 
A)  $x = - 7$ 
B)  $x = 7$ 
C)  $x = \sqrt { 7 }$ 
D)  $x = - \sqrt { 7 }$

Question 13

Write the function as a product of linear and irreducible quadratic factors, all with real coefficients.
-$$f ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } + 3 x - 10$$

Accepted Answer

A)  $( x - 2 ) \left( 2 x ^ { 2 } + x + - 5 \right)$ 
B)  $( x - 2 ) \left( 2 x ^ { 2 } + x + 5 \right)$ 
C)  $( x + 2 ) \left( 2 x ^ { 2 } + x + - 5 \right)$ 
D)  $( x + 2 ) \left( 2 x ^ { 2 } + x + 5 \right)$ 
A)  $( x - 2 ) \left( 2 x ^ { 2 } + x + - 5 \right)$ 
B)  $( x - 2 ) \left( 2 x ^ { 2 } + x + 5 \right)$ 
C)  $( x + 2 ) \left( 2 x ^ { 2 } + x + - 5 \right)$ 
D)  $( x + 2 ) \left( 2 x ^ { 2 } + x + 5 \right)$

Question 14

Describe the strength and direction of the linear correlation.
-

Accepted Answer

A)  Weak positive linear correlation 
B)  Strong positive linear correlation 
C)  Little or no linear correlation 
D)  Strong negative linear correlation 
A)  Weak positive linear correlation 
B)  Strong positive linear correlation 
C)  Little or no linear correlation 
D)  Strong negative linear correlation

Question 15

Write an equation for the quadratic function whose graph contains the given vertex and point.
-Vertex $( - 5 , - 5 )$, point $( - 2 , - 32 )$

Accepted Answer

A)  $P ( x ) = 3 x ^ { 2 } + 30 x - 5$ 
B)  $P ( x ) = - 3 x ^ { 2 } + 5 x - 5$ 
C)  $P ( x ) = - 2 x ^ { 2 } + 30 x + 80$ 
D)  $P ( x ) = - 3 x ^ { 2 } - 30 x - 80$ 
A)  $P ( x ) = 3 x ^ { 2 } + 30 x - 5$ 
B)  $P ( x ) = - 3 x ^ { 2 } + 5 x - 5$ 
C)  $P ( x ) = - 2 x ^ { 2 } + 30 x + 80$ 
D)  $P ( x ) = - 3 x ^ { 2 } - 30 x - 80$

Question 16

For the given function, find all asymptotes of the type indicated (if there are any)
-$f ( x ) = \frac { x + 4 } { 3 x ^ { 2 } + 6 x - 9 }$, slant

Accepted Answer

A)  $y = x + 3$ 
B)  $x = y + 3$ 
C)  None 
D)  $y = x + 4$ 
A)  $y = x + 3$ 
B)  $x = y + 3$ 
C)  None 
D)  $y = x + 4$

Question 17

Match the given graph with its polynomial function.Choose the one alternative that best completes the statement or answers the question.
-

Accepted Answer

A)  $f ( x ) = - x ^ { 5 } - 20 x ^ { 4 } - 100 x ^ { 2 } + 100 x$ 
B)  $f ( x ) = x ^ { 5 } - 10 x ^ { 4 } - 100 x ^ { 2 } + 100$ 
C)  $f ( x ) = - x ^ { 6 } + 10 x ^ { 4 } - 100 x ^ { 2 } - 100$ 
D)  $f ( x ) = - x ^ { 6 } + 20 x ^ { 4 } - 100 x ^ { 2 } + 100$ 
A)  $f ( x ) = - x ^ { 5 } - 20 x ^ { 4 } - 100 x ^ { 2 } + 100 x$ 
B)  $f ( x ) = x ^ { 5 } - 10 x ^ { 4 } - 100 x ^ { 2 } + 100$ 
C)  $f ( x ) = - x ^ { 6 } + 10 x ^ { 4 } - 100 x ^ { 2 } - 100$ 
D)  $f ( x ) = - x ^ { 6 } + 20 x ^ { 4 } - 100 x ^ { 2 } + 100$

Question 18

Solve the problem.
-The first column shows the independent variable (x). The second column shows the dependent variable (y).
 
 Use linear regression to predict the value of $y$ when $x = 5.5$.

Accepted Answer

A)  $52.16$ 
B)  $60.41$ 
C)  $57.66$ 
D)  $54.91$ 
A)  $52.16$ 
B)  $60.41$ 
C)  $57.66$ 
D)  $54.91$

Question 19

Find the vertex of the graph of the function.
-$$f ( x ) = - 2 x ^ { 2 } + 12 x - 23$$

Accepted Answer

A)  $( - 2 , - 5 )$ 
B)  $( 3 , - 5 )$ 
C)  $( 6 , - 2 )$ 
D)  $( - 2,6 )$ 
A)  $( - 2 , - 5 )$ 
B)  $( 3 , - 5 )$ 
C)  $( 6 , - 2 )$ 
D)  $( - 2,6 )$

Question 20

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the
polynomial in standard form.
-$5 , - 3$, and $- 1 + 4 i$

Accepted Answer

A)  $f ( x ) = x ^ { 4 } + 16 x ^ { 2 } - 64 x - 255$ 
B)  $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } - 20 x ^ { 2 } - 32 x - 255$ 
C)  $f ( x ) = x ^ { 4 } - 2 x ^ { 2 } - 64 x - 255$ 
D)  $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 20 x ^ { 2 } + 32 x + 255$ 
A)  $f ( x ) = x ^ { 4 } + 16 x ^ { 2 } - 64 x - 255$ 
B)  $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } - 20 x ^ { 2 } - 32 x - 255$ 
C)  $f ( x ) = x ^ { 4 } - 2 x ^ { 2 } - 64 x - 255$ 
D)  $f ( x ) = x ^ { 4 } - 4 x ^ { 3 } + 20 x ^ { 2 } + 32 x + 255$

Use the Rational Zeros Theorem to write a list of all potential rational zeros - $f ( x ) = - 2 x ^ { 4 } + 5 x ^ { 3 } + 6 x ^ { 2 } + 18$

For the given function, find all asymptotes of the type indicated (if there are any) - $f ( x ) = \frac { x - 9 } { x ^ { 2 } - 25 }$ , vertical

Match the polynomial function graph to the appropriate zeros and multiplicities. -

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. - $5 i$ and $\sqrt { 2 }$

Solve the problem. -The first column shows the independent variable (x). The second column shows the dependent variable (y). Find the linear regression model.

Use limits to describe the behavior of the rational function near the indicated asymptote. - $f ( x ) = \frac { 1 - 5 x } { x + 2 }$ Describe the behavior of the function near its horizontal asymptote (the end behavior).

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. - $f ( x ) = \frac { 1 } { 2 } x ^ { 7 }$

Determine the x values that cause the polynomial function to be (a) zero, (b) positive, and (c) negative. - $f ( x ) = ( x + 2 ) ( x + 1 ) ( x - 2 )$

Solve the problem. Round as appropriate. -The time T necessary to make an enlargement of a photo negative varies directly as the area A of the enlargement. If 60 seconds are required to make a 3-by-5 enlargement, find the time required for a 5-by-6 Enlargement.

Describe the strength and direction of the linear correlation. -

Find the axis of the graph of the function. - $f ( x ) = 4 ( x - \sqrt { 7 } ) ^ { 2 } + 5$

Write the function as a product of linear and irreducible quadratic factors, all with real coefficients. - $f ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } + 3 x - 10$

Describe the strength and direction of the linear correlation. -

Write an equation for the quadratic function whose graph contains the given vertex and point. -Vertex $( - 5 , - 5 )$ , point $( - 2 , - 32 )$

For the given function, find all asymptotes of the type indicated (if there are any) - $f ( x ) = \frac { x + 4 } { 3 x ^ { 2 } + 6 x - 9 }$ , slant

Match the given graph with its polynomial function.Choose the one alternative that best completes the statement or answers the question. -

Solve the problem. -The first column shows the independent variable (x). The second column shows the dependent variable (y). Use linear regression to predict the value of $y$ when $x = 5.5$ .

Find the vertex of the graph of the function. - $f ( x ) = - 2 x ^ { 2 } + 12 x - 23$

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. - $5 , - 3$ , and $- 1 + 4 i$

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

Exam 2: Polynomial, Power, and Rational Functions

Use the Rational Zeros Theorem to write a list of all potential rational zeros - f(x)=−2x4+5x3+6x2+18f ( x ) = - 2 x ^ { 4 } + 5 x ^ { 3 } + 6 x ^ { 2 } + 18f(x)=−2x4+5x3+6x2+18

For the given function, find all asymptotes of the type indicated (if there are any) - f(x)=x−9x2−25f ( x ) = \frac { x - 9 } { x ^ { 2 } - 25 }f(x)=x2−25x−9​ , vertical

Match the polynomial function graph to the appropriate zeros and multiplicities. -

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. - 5i5 i5i and 2\sqrt { 2 }2​

Solve the problem. -The first column shows the independent variable (x). The second column shows the dependent variable (y). Find the linear regression model.

Use limits to describe the behavior of the rational function near the indicated asymptote. - f(x)=1−5xx+2f ( x ) = \frac { 1 - 5 x } { x + 2 }f(x)=x+21−5x​ Describe the behavior of the function near its horizontal asymptote (the end behavior).

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)=12x7f ( x ) = \frac { 1 } { 2 } x ^ { 7 }f(x)=21​x7

Determine the x values that cause the polynomial function to be (a) zero, (b) positive, and (c) negative. - f(x)=(x+2)(x+1)(x−2)f ( x ) = ( x + 2 ) ( x + 1 ) ( x - 2 )f(x)=(x+2)(x+1)(x−2)

Solve the problem. Round as appropriate. -The time T necessary to make an enlargement of a photo negative varies directly as the area A of the enlargement. If 60 seconds are required to make a 3-by-5 enlargement, find the time required for a 5-by-6 Enlargement.

Describe the strength and direction of the linear correlation. -

Find the axis of the graph of the function. - f(x)=4(x−7)2+5f ( x ) = 4 ( x - \sqrt { 7 } ) ^ { 2 } + 5f(x)=4(x−7​)2+5

Write the function as a product of linear and irreducible quadratic factors, all with real coefficients. - f(x)=2x3−3x2+3x−10f ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } + 3 x - 10f(x)=2x3−3x2+3x−10

Describe the strength and direction of the linear correlation. -

Write an equation for the quadratic function whose graph contains the given vertex and point. -Vertex (−5,−5)( - 5 , - 5 )(−5,−5) , point (−2,−32)( - 2 , - 32 )(−2,−32)

For the given function, find all asymptotes of the type indicated (if there are any) - f(x)=x+43x2+6x−9f ( x ) = \frac { x + 4 } { 3 x ^ { 2 } + 6 x - 9 }f(x)=3x2+6x−9x+4​ , slant

Match the given graph with its polynomial function.Choose the one alternative that best completes the statement or answers the question. -

Solve the problem. -The first column shows the independent variable (x). The second column shows the dependent variable (y). Use linear regression to predict the value of yyy when x=5.5x = 5.5x=5.5 .

Find the vertex of the graph of the function. - f(x)=−2x2+12x−23f ( x ) = - 2 x ^ { 2 } + 12 x - 23f(x)=−2x2+12x−23

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. - 5,−35 , - 35,−3 , and −1+4i- 1 + 4 i−1+4i

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

Use the Rational Zeros Theorem to write a list of all potential rational zeros - $f ( x ) = - 2 x ^ { 4 } + 5 x ^ { 3 } + 6 x ^ { 2 } + 18$

For the given function, find all asymptotes of the type indicated (if there are any) - $f ( x ) = \frac { x - 9 } { x ^ { 2 } - 25 }$ , vertical

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. - $5 i$ and $\sqrt { 2 }$

Use limits to describe the behavior of the rational function near the indicated asymptote. - $f ( x ) = \frac { 1 - 5 x } { x + 2 }$ Describe the behavior of the function near its horizontal asymptote (the end behavior).

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. - $f ( x ) = \frac { 1 } { 2 } x ^ { 7 }$

Determine the x values that cause the polynomial function to be (a) zero, (b) positive, and (c) negative. - $f ( x ) = ( x + 2 ) ( x + 1 ) ( x - 2 )$

Find the axis of the graph of the function. - $f ( x ) = 4 ( x - \sqrt { 7 } ) ^ { 2 } + 5$

Write the function as a product of linear and irreducible quadratic factors, all with real coefficients. - $f ( x ) = 2 x ^ { 3 } - 3 x ^ { 2 } + 3 x - 10$

Write an equation for the quadratic function whose graph contains the given vertex and point. -Vertex $( - 5 , - 5 )$ , point $( - 2 , - 32 )$

For the given function, find all asymptotes of the type indicated (if there are any) - $f ( x ) = \frac { x + 4 } { 3 x ^ { 2 } + 6 x - 9 }$ , slant

Solve the problem. -The first column shows the independent variable (x). The second column shows the dependent variable (y). Use linear regression to predict the value of $y$ when $x = 5.5$ .

Find the vertex of the graph of the function. - $f ( x ) = - 2 x ^ { 2 } + 12 x - 23$

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form. - $5 , - 3$ , and $- 1 + 4 i$