Exam 4: Polynomials and Rational Functions

The population of a city has varied considerably in recent years. The data in the table relates the population P to time t, in years. Use a quadratic function fitted to the data to predict the population in year 10. Year, t Population, P 0 59,000 1 48,000 2 43,500 3 49,000 4 41,500 5 39,000 6 42,500

(Multiple Choice)

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Question 301

For the polynomial, one zero is given. Find all others. - $P ( x ) = x ^ { 4 } - 21 x ^ { 2 } - 100 ; - 2 i$

(Multiple Choice)

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Question 302

Identify the vertex of the parabola. - $f ( x ) = ( x - 3 ) ^ { 2 } + 9$

(Multiple Choice)

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Question 303

Find the domain and range of the function. $f ( x ) = - x ^ { 2 } - 12 x - 43$

(Multiple Choice)

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Question 304

$y \text { varies directly as the square of } z \text { and } y = 27 \text { when } z = 3 \text {. Find } y \text { when } z \text { is } 6 \text {. }$

(Multiple Choice)

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Question 305

Use the remainder theorem and synthetic division to find f(k). - $k = 4 ; f ( x ) = x ^ { 3 } - 2 x ^ { 2 } + 5 x - 2$

(Multiple Choice)

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Question 306

Determine which of the rational functions given below has the following feature(s). - $x$ -intercepts: $( - 3,0 )$ and $( 3,0 ) , y$ -intercept: $( 0,9 )$ , vertical asymptotes: $x = - 1$ and $x = 1$ , horizontal asymptote: $y = 1$

(Multiple Choice)

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Question 307

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = - 2 x ^ { 3 } + 2 x ^ { 2 } + 6 x - 3$

(Multiple Choice)

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Question 308

Find a polynomial function f(x) of least possible degree having the graph shown. -

(Multiple Choice)

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Question 309

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = \frac { 2 } { 3 } ; f ( x ) = 3 x ^ { 4 } + 5 x ^ { 2 } + 2$

(True/False)

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Question 310

Solve the inequality. Write the solution set in interval notation. - $x ^ { 2 } - 6 x - 16 > 0$

(Multiple Choice)

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Question 311

Give the domain and range for the rational function. Use interval notation. - $f ( x ) = - \frac { 2 } { ( x - 4 ) ^ { 2 } }$

(Multiple Choice)

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Question 312

In the following formula, f(x) is the minimum number of hours of studying required to attain a test score of x: $f ( x ) = \frac { 0.52 x } { 100.5 - x }$ How many hours of study are needed to score 96?

(Multiple Choice)

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Question 313

What is the range of the graph?

(Multiple Choice)

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Question 314

Give all possible rational zeros for the following polynomial. - $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 6 x - 24$

(Multiple Choice)

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Question 315

Give all possible rational zeros for the following polynomial. - $P ( x ) = - 2 x ^ { 4 } + 5 x ^ { 3 } + 3 x ^ { 2 } + 18$

(Multiple Choice)

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Question 316

Match the equation to the correct graph. - $y = - ( x + 4 ) ^ { 2 } + 6$

(Multiple Choice)

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Question 317

Sketch the graph of the parabola. -

(Multiple Choice)

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Question 318

Translate the given formula to an English phrase using the word "varies". - $\mathrm { A } = \frac { 1 } { 2 } \mathrm { bh }$ bh, where A is the area of a triangle with base b and height h

(Essay)

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Question 319

Use synthetic division to perform the division. $\frac { x ^ { 3 } - 1 } { x - 1 }$

(Multiple Choice)

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Question 320

The population of a city has varied considerably in recent years. The data in the table relates the population P to time t, in years. Use a quadratic function fitted to the data to predict the population in year 10. Year, t Population, P 0 59,000 1 48,000 2 43,500 3 49,000 4 41,500 5 39,000 6 42,500

For the polynomial, one zero is given. Find all others. - $P ( x ) = x ^ { 4 } - 21 x ^ { 2 } - 100 ; - 2 i$

Identify the vertex of the parabola. - $f ( x ) = ( x - 3 ) ^ { 2 } + 9$

Find the domain and range of the function. $f ( x ) = - x ^ { 2 } - 12 x - 43$

$y \text { varies directly as the square of } z \text { and } y = 27 \text { when } z = 3 \text {. Find } y \text { when } z \text { is } 6 \text {. }$

Use the remainder theorem and synthetic division to find f(k). - $k = 4 ; f ( x ) = x ^ { 3 } - 2 x ^ { 2 } + 5 x - 2$

Determine which of the rational functions given below has the following feature(s). - $x$ -intercepts: $( - 3,0 )$ and $( 3,0 ) , y$ -intercept: $( 0,9 )$ , vertical asymptotes: $x = - 1$ and $x = 1$ , horizontal asymptote: $y = 1$

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = - 2 x ^ { 3 } + 2 x ^ { 2 } + 6 x - 3$

Find a polynomial function f(x) of least possible degree having the graph shown. -

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = \frac { 2 } { 3 } ; f ( x ) = 3 x ^ { 4 } + 5 x ^ { 2 } + 2$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 2 } - 6 x - 16 > 0$

Give the domain and range for the rational function. Use interval notation. - $f ( x ) = - \frac { 2 } { ( x - 4 ) ^ { 2 } }$

In the following formula, f(x) is the minimum number of hours of studying required to attain a test score of x: $f ( x ) = \frac { 0.52 x } { 100.5 - x }$ How many hours of study are needed to score 96?

What is the range of the graph?

Give all possible rational zeros for the following polynomial. - $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 6 x - 24$

Give all possible rational zeros for the following polynomial. - $P ( x ) = - 2 x ^ { 4 } + 5 x ^ { 3 } + 3 x ^ { 2 } + 18$

Match the equation to the correct graph. - $y = - ( x + 4 ) ^ { 2 } + 6$

Sketch the graph of the parabola. -

Translate the given formula to an English phrase using the word "varies". - $\mathrm { A } = \frac { 1 } { 2 } \mathrm { bh }$ bh, where A is the area of a triangle with base b and height h

Use synthetic division to perform the division. $\frac { x ^ { 3 } - 1 } { x - 1 }$

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

Exam 4: Polynomials and Rational Functions

For the polynomial, one zero is given. Find all others. - P(x)=x4−21x2−100;−2iP ( x ) = x ^ { 4 } - 21 x ^ { 2 } - 100 ; - 2 iP(x)=x4−21x2−100;−2i

Identify the vertex of the parabola. - f(x)=(x−3)2+9f ( x ) = ( x - 3 ) ^ { 2 } + 9f(x)=(x−3)2+9

Find the domain and range of the function. f(x)=−x2−12x−43f ( x ) = - x ^ { 2 } - 12 x - 43f(x)=−x2−12x−43

Use the remainder theorem and synthetic division to find f(k). - k=4;f(x)=x3−2x2+5x−2k = 4 ; f ( x ) = x ^ { 3 } - 2 x ^ { 2 } + 5 x - 2k=4;f(x)=x3−2x2+5x−2

Determine which of the rational functions given below has the following feature(s). - xxx -intercepts: (−3,0)( - 3,0 )(−3,0) and (3,0),y( 3,0 ) , y(3,0),y -intercept: (0,9)( 0,9 )(0,9) , vertical asymptotes: x=−1x = - 1x=−1 and x=1x = 1x=1 , horizontal asymptote: y=1y = 1y=1

Find the correct end behavior diagram for the given polynomial function. - P(x)=−2x3+2x2+6x−3P ( x ) = - 2 x ^ { 3 } + 2 x ^ { 2 } + 6 x - 3P(x)=−2x3+2x2+6x−3

Find a polynomial function f(x) of least possible degree having the graph shown. -

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - k=23;f(x)=3x4+5x2+2k = \frac { 2 } { 3 } ; f ( x ) = 3 x ^ { 4 } + 5 x ^ { 2 } + 2k=32​;f(x)=3x4+5x2+2

Solve the inequality. Write the solution set in interval notation. - x2−6x−16>0x ^ { 2 } - 6 x - 16 > 0x2−6x−16>0

Give the domain and range for the rational function. Use interval notation. - f(x)=−2(x−4)2f ( x ) = - \frac { 2 } { ( x - 4 ) ^ { 2 } }f(x)=−(x−4)22​

In the following formula, f(x) is the minimum number of hours of studying required to attain a test score of x: f(x)=0.52x100.5−xf ( x ) = \frac { 0.52 x } { 100.5 - x }f(x)=100.5−x0.52x​ How many hours of study are needed to score 96?

What is the range of the graph?

Give all possible rational zeros for the following polynomial. - P(x)=x3−5x2+6x−24P ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 6 x - 24P(x)=x3−5x2+6x−24

Give all possible rational zeros for the following polynomial. - P(x)=−2x4+5x3+3x2+18P ( x ) = - 2 x ^ { 4 } + 5 x ^ { 3 } + 3 x ^ { 2 } + 18P(x)=−2x4+5x3+3x2+18

Match the equation to the correct graph. - y=−(x+4)2+6y = - ( x + 4 ) ^ { 2 } + 6y=−(x+4)2+6

Sketch the graph of the parabola. -

Translate the given formula to an English phrase using the word "varies". - A=12bh\mathrm { A } = \frac { 1 } { 2 } \mathrm { bh }A=21​bh bh, where A is the area of a triangle with base b and height h

Use synthetic division to perform the division. x3−1x−1\frac { x ^ { 3 } - 1 } { x - 1 }x−1x3−1​

Review of Basic Concepts

Equations and Inequalities

Graphs and Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Arithmetic Sequence: Common Difference and First n Terms

Filters

For the polynomial, one zero is given. Find all others. - $P ( x ) = x ^ { 4 } - 21 x ^ { 2 } - 100 ; - 2 i$

Identify the vertex of the parabola. - $f ( x ) = ( x - 3 ) ^ { 2 } + 9$

Find the domain and range of the function. $f ( x ) = - x ^ { 2 } - 12 x - 43$

Use the remainder theorem and synthetic division to find f(k). - $k = 4 ; f ( x ) = x ^ { 3 } - 2 x ^ { 2 } + 5 x - 2$

Determine which of the rational functions given below has the following feature(s). - $x$ -intercepts: $( - 3,0 )$ and $( 3,0 ) , y$ -intercept: $( 0,9 )$ , vertical asymptotes: $x = - 1$ and $x = 1$ , horizontal asymptote: $y = 1$

Find the correct end behavior diagram for the given polynomial function. - $P ( x ) = - 2 x ^ { 3 } + 2 x ^ { 2 } + 6 x - 3$

Use synthetic division to decide whether the given number k is a zero of the given polynomial function. - $k = \frac { 2 } { 3 } ; f ( x ) = 3 x ^ { 4 } + 5 x ^ { 2 } + 2$

Solve the inequality. Write the solution set in interval notation. - $x ^ { 2 } - 6 x - 16 > 0$

Give the domain and range for the rational function. Use interval notation. - $f ( x ) = - \frac { 2 } { ( x - 4 ) ^ { 2 } }$

In the following formula, f(x) is the minimum number of hours of studying required to attain a test score of x: $f ( x ) = \frac { 0.52 x } { 100.5 - x }$ How many hours of study are needed to score 96?

Give all possible rational zeros for the following polynomial. - $P ( x ) = x ^ { 3 } - 5 x ^ { 2 } + 6 x - 24$

Give all possible rational zeros for the following polynomial. - $P ( x ) = - 2 x ^ { 4 } + 5 x ^ { 3 } + 3 x ^ { 2 } + 18$

Match the equation to the correct graph. - $y = - ( x + 4 ) ^ { 2 } + 6$

Translate the given formula to an English phrase using the word "varies". - $\mathrm { A } = \frac { 1 } { 2 } \mathrm { bh }$ bh, where A is the area of a triangle with base b and height h

Use synthetic division to perform the division. $\frac { x ^ { 3 } - 1 } { x - 1 }$