Exam 4: Polynomial and Rational Functions

Use the equation and the corresponding graph for the quadratic function to find what is requested. - $f ( x ) = ( x - 1 ) ^ { 2 } - 1$ $Use the equation and the corresponding graph for the quadratic function to find what is requested. - f ( x ) = ( x - 1 ) ^ { 2 } - 1 Find the x-intercepts.$ Find the x-intercepts.

(Multiple Choice)

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Question 441

Factor f(x) into linear factors given that k is a zero of f(x). - $f ( x ) = x ^ { 4 } + 16 x ^ { 3 } + 62 x ^ { 2 } - 32 x - 128 ; k = - 8$ (multiplicity 2 $)$

(Multiple Choice)

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Question 442

Round your answer to two decimal places. -The time it takes to complete a certain job varies inversely to the number of people working on that job. If it takes 20 hours for 13 carpenters to frame a house, then how long will it take 25 carpenters To do the same job?

(Multiple Choice)

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Question 443

Solve the problem - $\mathrm { A } ( \mathrm { x } ) = - 0.015 \mathrm { x } ^ { 3 } + 1.05 \mathrm { x }$ gives the alcohol level in an average person's blood $\mathrm { x } \mathrm { hrs }$ after drinking $8 \mathrm { oz }$ of 100-proof whiskey. If the level exceeds $1.5$ units, a person is legally drunk. Would a person be drunk after 5 hours?

(Multiple Choice)

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Question 444

Translate the given formula to an English phrase using the word "varies". -What type of variation is suggested by the graph?

(Multiple Choice)

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Question 445

Use a graphing calculator to find the coordinates of the turning points of the graph of the polynomial function in the indicated domain interval. Give answers to the nearest hundredth. - $f ( x ) = x ^ { 3 } - 4 x + 3 ; [ 1,2 ]$

(Multiple Choice)

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Question 446

2Given the equation or other information for a parabola, find the matching description or graph. - f(x)=a+bx+c a<0;-4ac<0

(Multiple Choice)

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Question 447

Identify any vertical, horizontal, or oblique asymptotes in the graph of y = f(x). State the domain of f. -

(Multiple Choice)

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Question 448

Solve the problem -A coin is tossed upward from a balcony 176 feet high with an initial velocity of 16 feet per second, then its height after $t$ seconds is given by the equation $h ( t ) = - 16 t ^ { 2 } + 16 t + 176$ . During what interval of time will the coin be at a height of at least $80 \mathrm { ft }$ ?

(Multiple Choice)

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Question 449

Determine whether the statement is true or false. -If f(x) is a polynomial having only real coefficients and 1 - 4i is a zero of f(x), then -1 + 4i is also a zero.

(True/False)

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Question 450

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = 3 x ^ { 7 } + 4 x ^ { 2 } - 2$

(Multiple Choice)

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Question 451

Graph the polynomial function. Factor first if the expression is not in factored form. - $f(x)=-3 x(x-2)(x-1)$

(Multiple Choice)

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Question 452

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 3 x - 9$

(Multiple Choice)

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Question 453

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = 9 x ^ { 7 } + x ^ { 5 }$

(Multiple Choice)

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Question 454

Round to the nearest tenth unless indicated otherwise. -The cost of stainless steel tubing varies jointly as the length and the diameter of the tubing. If a 5 foot length with diameter 2 inches costs $\$ 48.00$ , how much will a 19 foot length with diameter 4 inches cost? Round to the nearest cent.

(Multiple Choice)

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Question 455

Solve the problem -If a rocket is propelled upward from ground level, its height in meters after $\mathrm { t }$ seconds is given by $\mathrm { h } ( \mathrm { t } ) = - 9.8 \mathrm { t } ^ { 2 } + 107.8 \mathrm { t }$ . During what interval of time will the rocket be higher than $294 \mathrm {~m} ?$

(Multiple Choice)

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Question 456

Solve. -The concentration of a certain gas molecule in the atmosphere serves as an indicator of industrial air pollution. The data in the following table show the relationship of the estimated concentration Of the molecule in the atmosphere, in parts per billion (ppb), to the year. Year Concentration (ppb) 0 2.4 10 3.4 25 4.0 49 3.6 Determine the linear, quadratic, cubic, or quartic function that best fits the data.

(Multiple Choice)

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Question 457

Round your answer to two decimal places. -The time T necessary to make an enlargement of a photo negative varies directly as the area A of the enlargement. If 105 seconds are required to make a 3-by-5 enlargement, find the time required For a 5-by-10 enlargement.

(Multiple Choice)

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Question 458

Use synthetic division to divide f(x) by x - k for the given value of k. Then express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - $f ( x ) = 2 x ^ { 5 } - x ^ { 4 } + 3 x ^ { 2 } - x + 5 ; \quad k = 1$

(Multiple Choice)

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Question 459

Give the equations of any vertical asymptotes. - $f ( x ) = \frac { x - 1 } { x ^ { 2 } + 8 x }$

(Multiple Choice)

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Question 460

Factor f(x) into linear factors given that k is a zero of f(x). - $f ( x ) = x ^ { 4 } + 16 x ^ { 3 } + 62 x ^ { 2 } - 32 x - 128 ; k = - 8$ (multiplicity 2 $)$

Round your answer to two decimal places. -The time it takes to complete a certain job varies inversely to the number of people working on that job. If it takes 20 hours for 13 carpenters to frame a house, then how long will it take 25 carpenters To do the same job?

Translate the given formula to an English phrase using the word "varies". -What type of variation is suggested by the graph?

Use a graphing calculator to find the coordinates of the turning points of the graph of the polynomial function in the indicated domain interval. Give answers to the nearest hundredth. - $f ( x ) = x ^ { 3 } - 4 x + 3 ; [ 1,2 ]$

2Given the equation or other information for a parabola, find the matching description or graph. - f(x)=a+bx+c a<0;-4ac<0

Identify any vertical, horizontal, or oblique asymptotes in the graph of y = f(x). State the domain of f. -

Determine whether the statement is true or false. -If f(x) is a polynomial having only real coefficients and 1 - 4i is a zero of f(x), then -1 + 4i is also a zero.

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = 3 x ^ { 7 } + 4 x ^ { 2 } - 2$

Graph the polynomial function. Factor first if the expression is not in factored form. - $f(x)=-3 x(x-2)(x-1)$

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 3 x - 9$

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = 9 x ^ { 7 } + x ^ { 5 }$

Round to the nearest tenth unless indicated otherwise. -The cost of stainless steel tubing varies jointly as the length and the diameter of the tubing. If a 5 foot length with diameter 2 inches costs $\$ 48.00$ , how much will a 19 foot length with diameter 4 inches cost? Round to the nearest cent.

Round your answer to two decimal places. -The time T necessary to make an enlargement of a photo negative varies directly as the area A of the enlargement. If 105 seconds are required to make a 3-by-5 enlargement, find the time required For a 5-by-10 enlargement.

Use synthetic division to divide f(x) by x - k for the given value of k. Then express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - $f ( x ) = 2 x ^ { 5 } - x ^ { 4 } + 3 x ^ { 2 } - x + 5 ; \quad k = 1$

Give the equations of any vertical asymptotes. - $f ( x ) = \frac { x - 1 } { x ^ { 2 } + 8 x }$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Exam 4: Polynomial and Rational Functions

Use the equation and the corresponding graph for the quadratic function to find what is requested. - f(x)=(x−1)2−1f ( x ) = ( x - 1 ) ^ { 2 } - 1f(x)=(x−1)2−1 Find the x-intercepts.

Factor f(x) into linear factors given that k is a zero of f(x). - f(x)=x4+16x3+62x2−32x−128;k=−8f ( x ) = x ^ { 4 } + 16 x ^ { 3 } + 62 x ^ { 2 } - 32 x - 128 ; k = - 8f(x)=x4+16x3+62x2−32x−128;k=−8 (multiplicity 2 )))

Round your answer to two decimal places. -The time it takes to complete a certain job varies inversely to the number of people working on that job. If it takes 20 hours for 13 carpenters to frame a house, then how long will it take 25 carpenters To do the same job?

Translate the given formula to an English phrase using the word "varies". -What type of variation is suggested by the graph?

Use a graphing calculator to find the coordinates of the turning points of the graph of the polynomial function in the indicated domain interval. Give answers to the nearest hundredth. - f(x)=x3−4x+3;[1,2]f ( x ) = x ^ { 3 } - 4 x + 3 ; [ 1,2 ]f(x)=x3−4x+3;[1,2]

2Given the equation or other information for a parabola, find the matching description or graph. - f(x)=a+bx+c a<0;-4ac<0

Identify any vertical, horizontal, or oblique asymptotes in the graph of y = f(x). State the domain of f. -

Determine whether the statement is true or false. -If f(x) is a polynomial having only real coefficients and 1 - 4i is a zero of f(x), then -1 + 4i is also a zero.

Find the correct end behavior diagram for the given polynomial function. - P(x)=3x7+4x2−2P ( x ) = 3 x ^ { 7 } + 4 x ^ { 2 } - 2P(x)=3x7+4x2−2

Graph the polynomial function. Factor first if the expression is not in factored form. - f(x)=−3x(x−2)(x−1)f(x)=-3 x(x-2)(x-1)f(x)=−3x(x−2)(x−1)

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - f(x)=x3+3x2−3x−9f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 3 x - 9f(x)=x3+3x2−3x−9

Find the zeros of the polynomial function and state the multiplicity of each. - f(x)=9x7+x5f ( x ) = 9 x ^ { 7 } + x ^ { 5 }f(x)=9x7+x5

Round your answer to two decimal places. -The time T necessary to make an enlargement of a photo negative varies directly as the area A of the enlargement. If 105 seconds are required to make a 3-by-5 enlargement, find the time required For a 5-by-10 enlargement.

Use synthetic division to divide f(x) by x - k for the given value of k. Then express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - f(x)=2x5−x4+3x2−x+5;k=1f ( x ) = 2 x ^ { 5 } - x ^ { 4 } + 3 x ^ { 2 } - x + 5 ; \quad k = 1f(x)=2x5−x4+3x2−x+5;k=1

Give the equations of any vertical asymptotes. - f(x)=x−1x2+8xf ( x ) = \frac { x - 1 } { x ^ { 2 } + 8 x }f(x)=x2+8xx−1​

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Trigonometric Functions

The Circular Functions and Their Graphs

Trigonometric Identities and Equations

Applications of Trigonometry

Systems and Matrices

Analytic Geometry

Further Topics in Algebra

Filters

Factor f(x) into linear factors given that k is a zero of f(x). - $f ( x ) = x ^ { 4 } + 16 x ^ { 3 } + 62 x ^ { 2 } - 32 x - 128 ; k = - 8$ (multiplicity 2 $)$

Use a graphing calculator to find the coordinates of the turning points of the graph of the polynomial function in the indicated domain interval. Give answers to the nearest hundredth. - $f ( x ) = x ^ { 3 } - 4 x + 3 ; [ 1,2 ]$

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = 3 x ^ { 7 } + 4 x ^ { 2 } - 2$

Graph the polynomial function. Factor first if the expression is not in factored form. - $f(x)=-3 x(x-2)(x-1)$

Use a graphing calculator to approximate the real zeros. Give each zero as a decimal to the nearest tenth. - $f ( x ) = x ^ { 3 } + 3 x ^ { 2 } - 3 x - 9$

Find the zeros of the polynomial function and state the multiplicity of each. - $f ( x ) = 9 x ^ { 7 } + x ^ { 5 }$

Use synthetic division to divide f(x) by x - k for the given value of k. Then express f(x) in the form f(x) = (x - k)q(x) + r for the given value of k. - $f ( x ) = 2 x ^ { 5 } - x ^ { 4 } + 3 x ^ { 2 } - x + 5 ; \quad k = 1$

Give the equations of any vertical asymptotes. - $f ( x ) = \frac { x - 1 } { x ^ { 2 } + 8 x }$