Question 1

Find the remainder when f(x) is divided by (x - k)
-$$f ( x ) = x ^ { 5 } + 4 x ^ { 4 } + 7 x ^ { 3 } - 5 x ^ { 2 } + 6 x + 5 ; k = - 3$$

Accepted Answer

A)  $- 171$ 
B)  $- 166$ 
C)  -161 
D)  $- 176$ 
A)  $- 171$ 
B)  $- 166$ 
C)  -161 
D)  $- 176$

Question 2

If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact.
-$$f ( x ) = - 15 x ^ { 5 } - 9 x ^ { 4 } - 6 x ^ { 3 } + 12$$

Accepted Answer

A)  Degree: 4 ; leading coefficient: $- 15$ 
B)  Degree: 5; leading coefficient: $- 15$ 
C)  Degree: $- 15$; leading coefficient: $- 6$ 
D)  Not a polynomial function. 
A)  Degree: 4 ; leading coefficient: $- 15$ 
B)  Degree: 5; leading coefficient: $- 15$ 
C)  Degree: $- 15$; leading coefficient: $- 6$ 
D)  Not a polynomial function.

Question 3

Find a cubic function with the given zeros.
-$\sqrt { 6 } , - \sqrt { 6 } , 2$

Accepted Answer

A)  $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } + 6 x + 12$ 
B)  $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 6 x + 12$ 
C)  $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 6 x + 12$ 
D)  $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 6 x - 12$ 
A)  $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } + 6 x + 12$ 
B)  $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 6 x + 12$ 
C)  $f ( x ) = x ^ { 3 } + 2 x ^ { 2 } - 6 x + 12$ 
D)  $f ( x ) = x ^ { 3 } - 2 x ^ { 2 } - 6 x - 12$

Question 4

Write a linear factorization of the function.
-$$f ( x ) = 9 x ^ { 3 } + 9 x$$

Accepted Answer

A)  $f ( x ) = 9 x ( x + i ) ^ { 2 }$ 
B)  $f ( x ) = x ( x + 9 i ) ( x - i )$ 
C)  $f ( x ) = 9 x ( x + 1 ) ^ { 2 }$ 
D)  $f ( x ) = 9 x ( x + i ) ( x - i )$ 
A)  $f ( x ) = 9 x ( x + i ) ^ { 2 }$ 
B)  $f ( x ) = x ( x + 9 i ) ( x - i )$ 
C)  $f ( x ) = 9 x ( x + 1 ) ^ { 2 }$ 
D)  $f ( x ) = 9 x ( x + i ) ( x - i )$

Question 5

Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or irrational.
-$$f ( x ) = 6 x ^ { 3 } + 25 x ^ { 2 } + 12 x - 7$$

Accepted Answer

A)  $- 1$ (rational), $- \frac { 7 } { 2 }$ (rational), $\frac { 1 } { 3 }$ (rational) 
B)  - 1 (rational), $\frac { 1 } { 3 }$ (rational), $\frac { 7 } { 2 }$ (rational) 
C)  $\frac { 1 } { 3 }$ (rational) (multiplicity 2 ); $- \frac { 7 } { 2 }$ (rational) 
D)  $- \frac { 1 } { 3 }$ (rational), $- \frac { 7 } { 2 }$ (rational), $\frac { 1 } { 3 }$ (rational) 
A)  $- 1$ (rational), $- \frac { 7 } { 2 }$ (rational), $\frac { 1 } { 3 }$ (rational) 
B)  - 1 (rational), $\frac { 1 } { 3 }$ (rational), $\frac { 7 } { 2 }$ (rational) 
C)  $\frac { 1 } { 3 }$ (rational) (multiplicity 2 ); $- \frac { 7 } { 2 }$ (rational) 
D)  $- \frac { 1 } { 3 }$ (rational), $- \frac { 7 } { 2 }$ (rational), $\frac { 1 } { 3 }$ (rational)

Question 6

Solve the polynomial inequality.
-$( x + 1 ) ( x - 1 ) ^ { 2 } > 0$

Accepted Answer

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

Question 7

Describe the strength and direction of the linear correlation.
-Each of several people of various ages was asked to choose his or her favorite number (1-100). Their ages and numbers are recorded in the following table:

Accepted Answer

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

Question 8

Solve the problem. Round as appropriate.
-The intensity I of light varies inversely as the square of the distance $D$ from the source. If the intensity of illumination on a screen $5 \mathrm { ft }$ from a light is 2 foot-candles, find the intensity on a screen $15 \mathrm { ft }$ from the light.

Accepted Answer

A)  $2 / 10$ foot-candle 
B)  $12 / 9$ foot-candles 
C)  $2 / 9$ foot-candle 
D)  2 foot-candles 
A)  $2 / 10$ foot-candle 
B)  $12 / 9$ foot-candles 
C)  $2 / 9$ foot-candle 
D)  2 foot-candles

Question 9

Determine the x values that cause the function to be (a) zero, (b) undefined, (c) positive, and (d) negative.
-$$f ( x ) = x \sqrt { x + 9 }$$

Accepted Answer

A)  (a) $\{ - 9,0 \}$, (b) $( \infty , - 9 )$, (c) $( - 9,0 )$, (d) $( 0 , \infty )$ 
B)  (a) $\{ - 9 \}$, (b) $( \infty , - 9 )$, (c) $( - 9 , \infty )$, (d) $\varnothing$ 
C)  (a) $\{ 0 \}$, (b) $( \infty, 0 )$, (c) $( 0 , \infty )$, (d) $\varnothing$ 
D)  (a) $\{ - 9,0 \}$, (b) $( - , - 9 )$, (c) $( 0 , \infty )$, (d) $( - 9,0 )$ 
A)  (a) $\{ - 9,0 \}$, (b) $( \infty , - 9 )$, (c) $( - 9,0 )$, (d) $( 0 , \infty )$ 
B)  (a) $\{ - 9 \}$, (b) $( \infty , - 9 )$, (c) $( - 9 , \infty )$, (d) $\varnothing$ 
C)  (a) $\{ 0 \}$, (b) $( \infty, 0 )$, (c) $( 0 , \infty )$, (d) $\varnothing$ 
D)  (a) $\{ - 9,0 \}$, (b) $( - , - 9 )$, (c) $( 0 , \infty )$, (d) $( - 9,0 )$

Question 10

Describe how the graph of the given function can be obtained by transforming the graph of the reciprocal function f(x) =
1/x.
-$$f ( x ) = \frac { - 3 } { x + 5 }$$

Accepted Answer

A)  Shift the graph of the reciprocal function left 5 units, reflect across the $x$-axis, and then stretch vertically by a factor of 3 . 
B)  Shift the graph of the reciprocal function left 5 units, and then stretch vertically by a factor of $- 3$. 
C)  Shift the graph of the reciprocal function right 5 units, and then stretch vertically by a factor of $- 3$. 
D)  Shift the graph of the reciprocal function right 5 units, reflect across the x-axis, and then stretch vertically by a factor of $- 3$. 
A)  Shift the graph of the reciprocal function left 5 units, reflect across the $x$-axis, and then stretch vertically by a factor of 3 . 
B)  Shift the graph of the reciprocal function left 5 units, and then stretch vertically by a factor of $- 3$. 
C)  Shift the graph of the reciprocal function right 5 units, and then stretch vertically by a factor of $- 3$. 
D)  Shift the graph of the reciprocal function right 5 units, reflect across the x-axis, and then stretch vertically by a factor of $- 3$.

Question 11

Write an equation for the linear function f satisfying the given conditions.
-$f ( 3 ) = 5$ and $f ( 6 ) = 6$

Accepted Answer

A)  $f ( x ) = \frac { 1 } { 3 } x + 4$ 
B)  $f ( x ) = \frac { 7 } { 3 } x - 2$ 
C)  $f ( x ) = \frac { 2 } { 3 } x + 3$ 
D)  $f ( x ) = \frac { 4 } { 3 } x - 2$ 
A)  $f ( x ) = \frac { 1 } { 3 } x + 4$ 
B)  $f ( x ) = \frac { 7 } { 3 } x - 2$ 
C)  $f ( x ) = \frac { 2 } { 3 } x + 3$ 
D)  $f ( x ) = \frac { 4 } { 3 } x - 2$

Question 12

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions.
-Zeros: $1 , - 2,3 ; f ( 2 ) = 20$

Accepted Answer

A)  $- 5 x ^ { 3 } + 10 x ^ { 2 } + 25 x - 30$ 
B)  $- 5 x ^ { 3 } - 20 x ^ { 2 } + 25 x - 30$ 
C)  $5 x ^ { 3 } + 20 x ^ { 2 } - 25 x + 30$ 
D)  $5 x ^ { 3 } - 10 x ^ { 2 } - 25 x + 30$ 
A)  $- 5 x ^ { 3 } + 10 x ^ { 2 } + 25 x - 30$ 
B)  $- 5 x ^ { 3 } - 20 x ^ { 2 } + 25 x - 30$ 
C)  $5 x ^ { 3 } + 20 x ^ { 2 } - 25 x + 30$ 
D)  $5 x ^ { 3 } - 10 x ^ { 2 } - 25 x + 30$

Question 13

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

Accepted Answer

A)  $f ( x ) = x ^ { 4 } - 2 x ^ { 2 } - 3 x + 12$ 
B)  $f ( x ) = - 3 x ^ { 5 } + 2 x ^ { 4 } - x ^ { 2 } + 2 x - 12$ 
C)  $f ( x ) = - 3 x ^ { 3 } - 10 x ^ { 2 } + 5 x + 12$ 
D)  $f ( x ) = 2 x ^ { 3 } - 12 x ^ { 2 } - 5 x - 12$ 
A)  $f ( x ) = x ^ { 4 } - 2 x ^ { 2 } - 3 x + 12$ 
B)  $f ( x ) = - 3 x ^ { 5 } + 2 x ^ { 4 } - x ^ { 2 } + 2 x - 12$ 
C)  $f ( x ) = - 3 x ^ { 3 } - 10 x ^ { 2 } + 5 x + 12$ 
D)  $f ( x ) = 2 x ^ { 3 } - 12 x ^ { 2 } - 5 x - 12$

Question 14

Divide f(x) by d(x), and write a summary statement in the form indicated.
-$f ( x ) = x ^ { 3 } + 5 ; d ( x ) = x + 2 \quad$ (Write answer in polynomial form)

Accepted Answer

A)  $f ( x ) = ( x + 2 ) \left( x ^ { 2 } - 2 x + 4 \right) - 8$ 
B)  $f ( x ) = ( x + 2 ) \left( x ^ { 2 } - 2 x + 4 \right) - 3$ 
C)  $f ( x ) = ( x + 2 ) \left( x ^ { 2 } + 2 x + 4 \right) - 8$ 
D)  $f ( x ) = ( x + 2 ) \left( x ^ { 2 } + 2 x + 4 \right) - 3$ 
A)  $f ( x ) = ( x + 2 ) \left( x ^ { 2 } - 2 x + 4 \right) - 8$ 
B)  $f ( x ) = ( x + 2 ) \left( x ^ { 2 } - 2 x + 4 \right) - 3$ 
C)  $f ( x ) = ( x + 2 ) \left( x ^ { 2 } + 2 x + 4 \right) - 8$ 
D)  $f ( x ) = ( x + 2 ) \left( x ^ { 2 } + 2 x + 4 \right) - 3$

Question 15

Use synthetic division to determine whether the number k is an upper or lower bound (as specified) for the real zeros of
the function f.
-$\mathrm { k } = - 1 ; \mathrm { f } ( \mathrm { x } ) = 4 \mathrm { x } ^ { 3 } + 5 \mathrm { x } ^ { 2 } - 4 \mathrm { x } - 3$; Lower bound?

Accepted Answer

A) True 
 B)False

Question 16

State the domain of the rational function.
-$$f ( x ) = \frac { x - 9 } { x ^ { 2 } + 4 }$$

Accepted Answer

A)  $( - \infty , - 3 ) \cup ( - 3,3 ) \cup ( 3 , \infty )$ 
B)  $( - \infty , - 4 ) \cup ( - 4 , \infty )$ 
C)  $( - \infty , 4 ) \cup ( 4 , \infty )$ 
D)  $( - \infty , \infty )$ 
A)  $( - \infty , - 3 ) \cup ( - 3,3 ) \cup ( 3 , \infty )$ 
B)  $( - \infty , - 4 ) \cup ( - 4 , \infty )$ 
C)  $( - \infty , 4 ) \cup ( 4 , \infty )$ 
D)  $( - \infty , \infty )$

Question 17

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)  $y = - 0.01 x ^ { 4 } + 0.29 x ^ { 3 } - 0.06 x ^ { 2 } - 0.23 x + 3.23$ 
B)  $y \approx 0.01 x ^ { 4 } - 0.09 x ^ { 3 } - 0.08 x ^ { 2 } - 0.23 x + 3.23$ 
C)  $y \approx - 0.01 x ^ { 4 } + 0.09 x ^ { 3 } - 0.08 x ^ { 2 } - 0.23 x + 3.23$ 
D)  $y \approx - 0.01 x ^ { 4 } + 0.29 x ^ { 3 } - 0.16 x ^ { 2 } - 0.23 x + 2.26$ 
A)  $y = - 0.01 x ^ { 4 } + 0.29 x ^ { 3 } - 0.06 x ^ { 2 } - 0.23 x + 3.23$ 
B)  $y \approx 0.01 x ^ { 4 } - 0.09 x ^ { 3 } - 0.08 x ^ { 2 } - 0.23 x + 3.23$ 
C)  $y \approx - 0.01 x ^ { 4 } + 0.09 x ^ { 3 } - 0.08 x ^ { 2 } - 0.23 x + 3.23$ 
D)  $y \approx - 0.01 x ^ { 4 } + 0.29 x ^ { 3 } - 0.16 x ^ { 2 } - 0.23 x + 2.26$

Question 18

Write the function as a product of linear and irreducible quadratic factors, all with real coefficients.
-$$f ( x ) = 3 x ^ { 3 } + 10 x ^ { 2 } + 6 x + 9$$

Accepted Answer

A)  $( x + 3 ) \left( 3 x ^ { 2 } + 2 x - 3 \right)$ 
B)  $( x + 3 ) \left( 3 x ^ { 2 } + x + 3 \right)$ 
C)  $( x - 3 ) \left( 3 x ^ { 2 } + x + 3 \right)$ 
D)  $( x + 3 ) \left( 2 x ^ { 2 } + x + 3 \right)$ 
A)  $( x + 3 ) \left( 3 x ^ { 2 } + 2 x - 3 \right)$ 
B)  $( x + 3 ) \left( 3 x ^ { 2 } + x + 3 \right)$ 
C)  $( x - 3 ) \left( 3 x ^ { 2 } + x + 3 \right)$ 
D)  $( x + 3 ) \left( 2 x ^ { 2 } + x + 3 \right)$

Question 19

Determine if the function is a monomial function (given that c and k represent constants). If it is, state the degree and
leading coefficient.
-$$f ( x ) = - 5 \cdot x ^ { 4 }$$

Accepted Answer

A)  Not a monomial function 
B)  Degree is 4; leading coefficient is $- 5$ 
C)  Degree is 4 ; leading coefficient is 5 
D)  Degree is $- 5$; leading coefficient is 4 
A)  Not a monomial function 
B)  Degree is 4; leading coefficient is $- 5$ 
C)  Degree is 4 ; leading coefficient is 5 
D)  Degree is $- 5$; leading coefficient is 4

Question 20

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.
-$$f ( x ) = \frac { 2 } { x ^ { 2 } - 2 x - 3 }$$

Accepted Answer

@#LAT-DLM&-intercept: none
@#LAT-DLM&-intercept: @#LAT-DLM&

Find the remainder when f(x) is divided by (x - k) - $f ( x ) = x ^ { 5 } + 4 x ^ { 4 } + 7 x ^ { 3 } - 5 x ^ { 2 } + 6 x + 5 ; k = - 3$

If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact. - $f ( x ) = - 15 x ^ { 5 } - 9 x ^ { 4 } - 6 x ^ { 3 } + 12$

Find a cubic function with the given zeros. - $\sqrt { 6 } , - \sqrt { 6 } , 2$

Write a linear factorization of the function. - $f ( x ) = 9 x ^ { 3 } + 9 x$

Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or irrational. - $f ( x ) = 6 x ^ { 3 } + 25 x ^ { 2 } + 12 x - 7$

Solve the polynomial inequality. - $( x + 1 ) ( x - 1 ) ^ { 2 } > 0$

Describe the strength and direction of the linear correlation. -Each of several people of various ages was asked to choose his or her favorite number (1-100). Their ages and numbers are recorded in the following table:

Solve the problem. Round as appropriate. -The intensity I of light varies inversely as the square of the distance $D$ from the source. If the intensity of illumination on a screen $5 \mathrm { ft }$ from a light is 2 foot-candles, find the intensity on a screen $15 \mathrm { ft }$ from the light.

Determine the x values that cause the function to be (a) zero, (b) undefined, (c) positive, and (d) negative. - $f ( x ) = x \sqrt { x + 9 }$

Describe how the graph of the given function can be obtained by transforming the graph of the reciprocal function f(x) = 1/x. - $f ( x ) = \frac { - 3 } { x + 5 }$

Write an equation for the linear function f satisfying the given conditions. - $f ( 3 ) = 5$ and $f ( 6 ) = 6$

Find a polynomial of degree 3 with real coefficients that satisfies the given conditions. -Zeros: $1 , - 2,3 ; f ( 2 ) = 20$

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

Divide f(x) by d(x), and write a summary statement in the form indicated. - $f ( x ) = x ^ { 3 } + 5 ; d ( x ) = x + 2 \quad$ (Write answer in polynomial form)

Use synthetic division to determine whether the number k is an upper or lower bound (as specified) for the real zeros of the function f. - $\mathrm { k } = - 1 ; \mathrm { f } ( \mathrm { x } ) = 4 \mathrm { x } ^ { 3 } + 5 \mathrm { x } ^ { 2 } - 4 \mathrm { x } - 3$ ; Lower bound?

State the domain of the rational function. - $f ( x ) = \frac { x - 9 } { x ^ { 2 } + 4 }$

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

Write the function as a product of linear and irreducible quadratic factors, all with real coefficients. - $f ( x ) = 3 x ^ { 3 } + 10 x ^ { 2 } + 6 x + 9$

Determine if the function is a monomial function (given that c and k represent constants). If it is, state the degree and leading coefficient. - $f ( x ) = - 5 \cdot x ^ { 4 }$

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An Introduction to Calculus: Limits, Derivatives, and Integrals

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Exam 2: Polynomial, Power, and Rational Functions

Find the remainder when f(x) is divided by (x - k) - f(x)=x5+4x4+7x3−5x2+6x+5;k=−3f ( x ) = x ^ { 5 } + 4 x ^ { 4 } + 7 x ^ { 3 } - 5 x ^ { 2 } + 6 x + 5 ; k = - 3f(x)=x5+4x4+7x3−5x2+6x+5;k=−3

If the following is a polynomial function, then state its degree and leading coefficient. If it is not, then state this fact. - f(x)=−15x5−9x4−6x3+12f ( x ) = - 15 x ^ { 5 } - 9 x ^ { 4 } - 6 x ^ { 3 } + 12f(x)=−15x5−9x4−6x3+12

Find a cubic function with the given zeros. - 6,−6,2\sqrt { 6 } , - \sqrt { 6 } , 26​,−6​,2

Write a linear factorization of the function. - f(x)=9x3+9xf ( x ) = 9 x ^ { 3 } + 9 xf(x)=9x3+9x

Find all of the real zeros of the function. Give exact values whenever possible. Identify each zero as rational or irrational. - f(x)=6x3+25x2+12x−7f ( x ) = 6 x ^ { 3 } + 25 x ^ { 2 } + 12 x - 7f(x)=6x3+25x2+12x−7

Solve the polynomial inequality. - (x+1)(x−1)2>0( x + 1 ) ( x - 1 ) ^ { 2 } > 0(x+1)(x−1)2>0