Question 1

Use the Rational Zeros Theorem to write a list of all potential rational zeros
-$$f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 8 x - 24$$

Accepted Answer

A)  $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 12 , \pm 24$ 
B)  $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 24$ 
C)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 8 , \pm 12 , \pm 24$ 
D)  $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 8 , \pm 12 , \pm 24$ 
A)  $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 12 , \pm 24$ 
B)  $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 24$ 
C)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 8 , \pm 12 , \pm 24$ 
D)  $\pm 1 , \pm 2 , \pm 3 , \pm 4 , \pm 6 , \pm 8 , \pm 12 , \pm 24$

Question 2

Describe how the graph of the given function can be obtained by transforming the graph of the reciprocal function f(x) =
1/x.
-$$f ( x ) = \frac { 2 } { x + 6 }$$

Accepted Answer

A)  Shift the graph of the reciprocal function right 6 units, and then stretch vertically by a factor of 2 . 
B)  Shift the graph of the reciprocal function left 6 units, and then shrink vertically by a factor of $\frac { 1 } { 2 }$. 
C)  Shift the graph of the reciprocal function left 6 units, and then stretch horizontally by a factor of 2 . 
D)  Shift the graph of the reciprocal function left 6 units, and then stretch vertically by a factor of 2 . 
A)  Shift the graph of the reciprocal function right 6 units, and then stretch vertically by a factor of 2 . 
B)  Shift the graph of the reciprocal function left 6 units, and then shrink vertically by a factor of $\frac { 1 } { 2 }$. 
C)  Shift the graph of the reciprocal function left 6 units, and then stretch horizontally by a factor of 2 . 
D)  Shift the graph of the reciprocal function left 6 units, and then stretch vertically by a factor of 2 .

Question 3

Solve the problem.
-The first column shows the independent variable $( \mathrm { x } )$. The second column shows the dependent variable (y).

Find the quadratic regression model.

Accepted Answer

A)  $y = - 0.04 x ^ { 2 } - 7.80 x + 92.60$ 
B)  $y = - 0.04 x ^ { 2 } - 8.80 x + 94.60$ 
C)  $y = - 0.03 x ^ { 2 } - 7.80 x + 94.60$ 
D)  $y = - 0.03 x ^ { 2 } - 8.80 x + 92.60$ 
A)  $y = - 0.04 x ^ { 2 } - 7.80 x + 92.60$ 
B)  $y = - 0.04 x ^ { 2 } - 8.80 x + 94.60$ 
C)  $y = - 0.03 x ^ { 2 } - 7.80 x + 94.60$ 
D)  $y = - 0.03 x ^ { 2 } - 8.80 x + 92.60$

Question 4

Write the polynomial in standard form and identify the zeros of the function.
-$$f ( x ) = ( x - 5 i ) ( x + 5 i )$$

Accepted Answer

A)  $f ( x ) = x ^ { 2 } - 25 ;$ zeros $\pm 5 i$ 
B)  $f ( x ) = x ^ { 2 } + 25$; zeros $\pm 5 i$ 
C)  $f ( x ) = x ^ { 2 } + 25$; zeros $\pm 5$ 
D)  $f ( x ) = x ^ { 2 } + 5 i x + 25 ;$ zeros $\pm 5$ 
A)  $f ( x ) = x ^ { 2 } - 25 ;$ zeros $\pm 5 i$ 
B)  $f ( x ) = x ^ { 2 } + 25$; zeros $\pm 5 i$ 
C)  $f ( x ) = x ^ { 2 } + 25$; zeros $\pm 5$ 
D)  $f ( x ) = x ^ { 2 } + 5 i x + 25 ;$ zeros $\pm 5$

Question 5

Data are given for y as a power function of x. Write an equation for the power function, and state its power and constant
of variation.
-

Accepted Answer

A)  $\mathrm { y } = - \frac { 16 } { \mathrm { x } ^ { - 2 } } ;$ Power $= - 2 ;$ constant of variation $= - 16$ 
B)  $y = - 16 x$; Power $= 1$; constant of variation $= - 16$ 
C)  $y = - \frac { 16 } { x }$; Power $= - 1$; constant of variation $= - 16$ 
D)  $\mathrm { y } = \frac { 16 } { \mathrm { x } ^ { 2 } } ;$ Power $= - 3 ;$ constant of variation $= 16$ 
A)  $\mathrm { y } = - \frac { 16 } { \mathrm { x } ^ { - 2 } } ;$ Power $= - 2 ;$ constant of variation $= - 16$ 
B)  $y = - 16 x$; Power $= 1$; constant of variation $= - 16$ 
C)  $y = - \frac { 16 } { x }$; Power $= - 1$; constant of variation $= - 16$ 
D)  $\mathrm { y } = \frac { 16 } { \mathrm { x } ^ { 2 } } ;$ Power $= - 3 ;$ constant of variation $= 16$

Question 6

Solve the problem.
-A piece of rectangular sheet metal is 21 inches wide. It is to be made into a rain gutter by turning up equal edges to form parallel sides. Let x represent the length of each of the parallel sides. For what value of x will the area of
The cross section be a maximum (and thus maximize the amount of water that the gutter will hold)? If necessary,
Round to 2 decimal places.

Accepted Answer

A)  10.5 
B)  5.25 
C)  84 
D)  42 
A)  10.5 
B)  5.25 
C)  84 
D)  42

Question 7

Find the requested function.
-Find the cubic function with the given table of values.

Accepted Answer

A)  $f ( x ) = - 3 ( x + 4 ) ( x - 3 ) ( x + 7 )$ 
B)  $f ( x ) = - 3 ( x - 4 ) ( x + 3 ) ( x + 7 )$ 
C)  $f ( x ) = - 3 ( x + 4 ) ( x - 3 ) ( x - 7 )$ 
D)  $f ( x ) = ( x + 4 ) ( x - 3 ) ( x - 7 )$ 
A)  $f ( x ) = - 3 ( x + 4 ) ( x - 3 ) ( x + 7 )$ 
B)  $f ( x ) = - 3 ( x - 4 ) ( x + 3 ) ( x + 7 )$ 
C)  $f ( x ) = - 3 ( x + 4 ) ( x - 3 ) ( x - 7 )$ 
D)  $f ( x ) = ( x + 4 ) ( x - 3 ) ( x - 7 )$

Question 8

Determine if the function is a power function. If it is, then state the power and constant of variation.
-$$f ( x ) = 6 \cdot 7 ^ { x }$$

Accepted Answer

A)  Not a power function 
B)  Power is 7; constant of variation is 6 
C)  Power is x; constant of variation is 42 
D)  Power is x; constant of variation is 6 
A)  Not a power function 
B)  Power is 7; constant of variation is 6 
C)  Power is x; constant of variation is 42 
D)  Power is x; constant of variation is 6

Question 9

Write an equation for the quadratic function whose graph contains the given vertex and point.
-Vertex $( - 5,6 )$, point $( 0,56 )$ (Write your answer in vertex form.)

Accepted Answer

A)  $\mathrm { P } ( \mathrm { x } ) = 2 ( \mathrm { x } + 5 ) ^ { 2 } + 6$ 
B)  $P ( x ) = 2 ( x - 5 ) ^ { 2 } + 6$ 
C)  $P ( x ) = \frac { 62 } { 25 } ( x + 5 ) ^ { 2 } - 6$ 
D)  $P ( x ) = ( x + 5 ) ^ { 2 } + 31$ 
A)  $\mathrm { P } ( \mathrm { x } ) = 2 ( \mathrm { x } + 5 ) ^ { 2 } + 6$ 
B)  $P ( x ) = 2 ( x - 5 ) ^ { 2 } + 6$ 
C)  $P ( x ) = \frac { 62 } { 25 } ( x + 5 ) ^ { 2 } - 6$ 
D)  $P ( x ) = ( x + 5 ) ^ { 2 } + 31$

Question 10

Use the Rational Zeros Theorem to write a list of all potential rational zeros
-$$f ( x ) = 13 x ^ { 3 } + 23 x ^ { 2 } + 2 x - 26$$

Accepted Answer

A)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 13 , \pm \frac { 13 } { 2 } , \pm \frac { 1 } { 13 } , \pm \frac { 1 } { 26 }$ 
B)  $\pm 1 , \pm 2 , \pm 13 , \pm 26$ 
C)  $\pm 1 , \pm \frac { 1 } { 13 } , \pm 2 , \pm 13 , \pm 26$ 
D)  $\pm 1 , \pm \frac { 1 } { 13 } , \pm 2 , \pm \frac { 2 } { 13 } , \pm 13 , \pm 26$ 
A)  $\pm 1 , \pm \frac { 1 } { 2 } , \pm 13 , \pm \frac { 13 } { 2 } , \pm \frac { 1 } { 13 } , \pm \frac { 1 } { 26 }$ 
B)  $\pm 1 , \pm 2 , \pm 13 , \pm 26$ 
C)  $\pm 1 , \pm \frac { 1 } { 13 } , \pm 2 , \pm 13 , \pm 26$ 
D)  $\pm 1 , \pm \frac { 1 } { 13 } , \pm 2 , \pm \frac { 2 } { 13 } , \pm 13 , \pm 26$

Question 11

Provide an appropriate response.
-Suppose that $a$, $b$, and $c$ are real numbers and that the polynomial function $\mathrm { f }$ may be expressed in factored form as $f ( x ) = ( 13 x - 7 ) ( 14 x + 5 ) \left( a x ^ { 2 } + b x + c \right)$. If $b ^ { 2 } - 4 a c = 169$, determine the number of rational, irrational, and imaginary zeros that $f$ has.

Accepted Answer

A)  2 rational zeros, 2 irrational zeros, 0 imaginary zeros 
B)  4 rational zeros, 0 irrational zeros, 0 imaginary zeros 
C)  2 rational zeros, 0 irrational zeros, 2 imaginary zeros 
D)  0 rational zeros, 0 irrational zeros, 4 imaginary zeros 
A)  2 rational zeros, 2 irrational zeros, 0 imaginary zeros 
B)  4 rational zeros, 0 irrational zeros, 0 imaginary zeros 
C)  2 rational zeros, 0 irrational zeros, 2 imaginary zeros 
D)  0 rational zeros, 0 irrational zeros, 4 imaginary zeros

Question 12

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

Accepted Answer

A)  Degree: 15; leading coefficient: 6 
B)  Not a polynomial function. 
C)  Degree: 6; leading coefficient: 15 
D)  Degree: 7; leading coefficient: 15 
A)  Degree: 15; leading coefficient: 6 
B)  Not a polynomial function. 
C)  Degree: 6; leading coefficient: 15 
D)  Degree: 7; leading coefficient: 15

Question 13

Find the zeros of the function.
-$$f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - 35 x - 150$$

Accepted Answer

A)  $5 , - 5$, and 6 
B)  5,5 , and $- 6$ 
C)  $- 5 , - 5$, and 6 
D)  $- 5,5$, and $- 6$ 
A)  $5 , - 5$, and 6 
B)  5,5 , and $- 6$ 
C)  $- 5 , - 5$, and 6 
D)  $- 5,5$, and $- 6$

Question 14

Find the zeros of the polynomial function and state the multiplicity of each.
-$$f ( x ) = ( x + 3 ) ^ { 2 } ( x - 1 )$$

Accepted Answer

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

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.
-$$I = P R T \text {, where } I \text { is the simple interest on a principal of } P \text { dollars at a rate of interest } R \text { per year }$$

Accepted Answer

Simple interest is d

Question 16

Divide f(x) by d(x), and write a summary statement in the form indicated.
-$f ( x ) = x ^ { 3 } - 4 ; d ( x ) = x + 6 \quad$ (Write answer in fraction form)

Accepted Answer

A)  $\frac { f ( x ) } { ( x + 6 ) } = \left( x ^ { 2 } - 6 x + 36 \right) + \frac { - 216 } { ( x + 6 ) }$ 
B)  $\frac { f ( x ) } { ( x + 6 ) } = \left( x ^ { 2 } + 6 x + 36 \right) + \frac { - 216 } { ( x + 6 ) }$ 
C)  $\frac { f ( x ) } { ( x + 6 ) } = \left( x ^ { 2 } + 6 x + 36 \right) + \frac { - 220 } { ( x + 6 ) }$ 
D)  $\frac { f ( x ) } { ( x + 6 ) } = \left( x ^ { 2 } - 6 x + 36 \right) + \frac { - 220 } { ( x + 6 ) }$ 
A)  $\frac { f ( x ) } { ( x + 6 ) } = \left( x ^ { 2 } - 6 x + 36 \right) + \frac { - 216 } { ( x + 6 ) }$ 
B)  $\frac { f ( x ) } { ( x + 6 ) } = \left( x ^ { 2 } + 6 x + 36 \right) + \frac { - 216 } { ( x + 6 ) }$ 
C)  $\frac { f ( x ) } { ( x + 6 ) } = \left( x ^ { 2 } + 6 x + 36 \right) + \frac { - 220 } { ( x + 6 ) }$ 
D)  $\frac { f ( x ) } { ( x + 6 ) } = \left( x ^ { 2 } - 6 x + 36 \right) + \frac { - 220 } { ( x + 6 ) }$

Question 17

Solve the inequality.
-$$\frac { x ^ { 2 } - 81 } { x ^ { 2 } + 81 } \geq 0$$

Accepted Answer

A)  $[ - 9,9 ]$ 
B)  $( - \infty , - 81 ] \cup [ 81 , \infty )$ 
C)  $[ 9 , \infty )$ 
D)  $( - \infty , - 9 ] \cup [ 9 , \infty )$ 
A)  $[ - 9,9 ]$ 
B)  $( - \infty , - 81 ] \cup [ 81 , \infty )$ 
C)  $[ 9 , \infty )$ 
D)  $( - \infty , - 9 ] \cup [ 9 , \infty )$

Question 18

State the power and constant of variation for the function, and then analyze it.
-$$f ( x ) = - \frac { 4 } { x ^ { 2 } }$$

Accepted Answer

Power is @#LAT-DLM&; constant of variation is @#LAT-DLM&; Do

Question 19

Determine if the function is a power function. If it is, then state the power and constant of variation.
-$$f ( x ) = 5 x ^ { 2 / 5 }$$

Accepted Answer

A)  Power is $\frac { 2 } { 5 }$; constant of variation is 5 
B)  Power is $\frac { 5 } { 2 }$; constant of variation is 5 
C)  Not a power function 
D)  Power is 5; constant of variation is $\frac { 2 } { 5 }$ 
A)  Power is $\frac { 2 } { 5 }$; constant of variation is 5 
B)  Power is $\frac { 5 } { 2 }$; constant of variation is 5 
C)  Not a power function 
D)  Power is 5; constant of variation is $\frac { 2 } { 5 }$

Question 20

Solve the problem.
-If a rocket is propelled upward from ground level, its height in meters after $t$ seconds is given by $h = - 9.8 \mathrm { t } ^ { 2 } + 98 \mathrm { t }$. During what interval of time will the rocket be higher than $205.8 \mathrm {~m}$ ?

Accepted Answer

A)  $7 < t < 6$ 
B)  $0 < t < 3$ 
C)  $3 < t < 7$ 
D)  $6 < t < 10$ 
A)  $7 < t < 6$ 
B)  $0 < t < 3$ 
C)  $3 < t < 7$ 
D)  $6 < t < 10$

Use the Rational Zeros Theorem to write a list of all potential rational zeros - $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 8 x - 24$

Describe how the graph of the given function can be obtained by transforming the graph of the reciprocal function f(x) = 1/x. - $f ( x ) = \frac { 2 } { x + 6 }$

Write the polynomial in standard form and identify the zeros of the function. - $f ( x ) = ( x - 5 i ) ( x + 5 i )$

Data are given for y as a power function of x. Write an equation for the power function, and state its power and constant of variation. -

Find the requested function. -Find the cubic function with the given table of values.

Determine if the function is a power function. If it is, then state the power and constant of variation. - $f ( x ) = 6 \cdot 7 ^ { x }$

Write an equation for the quadratic function whose graph contains the given vertex and point. -Vertex $( - 5,6 )$ , point $( 0,56 )$ (Write your answer in vertex form.)

Use the Rational Zeros Theorem to write a list of all potential rational zeros - $f ( x ) = 13 x ^ { 3 } + 23 x ^ { 2 } + 2 x - 26$

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

Find the zeros of the function. - $f ( x ) = x ^ { 3 } + 4 x ^ { 2 } - 35 x - 150$

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = ( x + 3 ) ^ { 2 } ( x - 1 )$

Divide f(x) by d(x), and write a summary statement in the form indicated. - $f ( x ) = x ^ { 3 } - 4 ; d ( x ) = x + 6 \quad$ (Write answer in fraction form)

Solve the inequality. - $\frac { x ^ { 2 } - 81 } { x ^ { 2 } + 81 } \geq 0$

State the power and constant of variation for the function, and then analyze it. - $f ( x ) = - \frac { 4 } { x ^ { 2 } }$

Determine if the function is a power function. If it is, then state the power and constant of variation. - $f ( x ) = 5 x ^ { 2 / 5 }$

Solve the problem. -If a rocket is propelled upward from ground level, its height in meters after $t$ seconds is given by $h = - 9.8 \mathrm { t } ^ { 2 } + 98 \mathrm { t }$ . During what interval of time will the rocket be higher than $205.8 \mathrm {~m}$ ?

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Exam 2: Polynomial, Power, and Rational Functions

Use the Rational Zeros Theorem to write a list of all potential rational zeros - f(x)=x3−10x2+8x−24f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 8 x - 24f(x)=x3−10x2+8x−24

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)=2x+6f ( x ) = \frac { 2 } { x + 6 }f(x)=x+62​

Solve the problem. -The first column shows the independent variable (x)( \mathrm { x } )(x) . The second column shows the dependent variable (y). Find the quadratic regression model.

Write the polynomial in standard form and identify the zeros of the function. - f(x)=(x−5i)(x+5i)f ( x ) = ( x - 5 i ) ( x + 5 i )f(x)=(x−5i)(x+5i)