Exam 3: Polynomial and Rational Functions

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. - $f ( x ) = - 9 x ^ { 4 } + 2 x ^ { 3 } + 8 x + 1 ; [ 1,2 ]$

(Multiple Choice)

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Question 301

Find the domain of the rational function. - $f ( x ) = \frac { 8 x } { x - 3 }$

(Multiple Choice)

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Question 302

Solve the problem. - $x ^ { 2 } - 3 x \geq - 2$

(Multiple Choice)

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Question 303

Solve the problem. - $( b - 2 ) ( b - 3 ) ( b - 4 ) < 0$

(Multiple Choice)

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Question 304

Find all zeros of the function and write the polynomial as a product of linear factors. - $f ( x ) = 3 x ^ { 4 } - 7 x ^ { 3 } + 29 x ^ { 2 } - 63 x + 18$

(Multiple Choice)

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Question 305

Give the equation of the horizontal asymptote, if any, of the function. - $f ( x ) = \frac { x + 9 } { x ^ { 2 } - 25 }$

(Multiple Choice)

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Question 306

Find the vertical asymptotes of the rational function. - $h ( x ) = \frac { x + 11 } { x ^ { 2 } - 16 x }$

(Multiple Choice)

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Question 307

Give the equation of the horizontal asymptote, if any, of the function. - $h ( x ) = \frac { 2 x ^ { 3 } - 8 x - 9 } { 7 x + 8 }$

(Multiple Choice)

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Question 308

Use transformations of the graph o $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ to graph the function. - $f ( x ) = 4 - ( x - 2 ) ^ { 5 }$ $Use transformations of the graph o y = x ^ { 4 } \text { or } y = x ^ { 5 } to graph the function. - f ( x ) = 4 - ( x - 2 ) ^ { 5 } A) B) C) D)$ A) $Use transformations of the graph o y = x ^ { 4 } \text { or } y = x ^ { 5 } to graph the function. - f ( x ) = 4 - ( x - 2 ) ^ { 5 } A) B) C) D)$ B) $Use transformations of the graph o y = x ^ { 4 } \text { or } y = x ^ { 5 } to graph the function. - f ( x ) = 4 - ( x - 2 ) ^ { 5 } A) B) C) D)$ C) $Use transformations of the graph o y = x ^ { 4 } \text { or } y = x ^ { 5 } to graph the function. - f ( x ) = 4 - ( x - 2 ) ^ { 5 } A) B) C) D)$ D) $Use transformations of the graph o y = x ^ { 4 } \text { or } y = x ^ { 5 } to graph the function. - f ( x ) = 4 - ( x - 2 ) ^ { 5 } A) B) C) D)$

(Multiple Choice)

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Question 309

Form a polynomial f(x) with real coefficients having the given degree and zeros. -Degree: 4; zeros: $- 1,2$ , and $1 - 2 \mathrm { i }$ .

(Multiple Choice)

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Question 310

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = \sqrt { x } ( \sqrt { x } - 5 )$

(Multiple Choice)

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Question 311

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. - $f ( x ) = \left( x + \frac { 1 } { 4 } \right) ^ { 2 } \left( x ^ { 2 } + 7 \right) ^ { 3 }$

(Multiple Choice)

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Question 312

Find the vertical asymptotes of the rational function. - $f ( x ) = \frac { x + 2 } { x ^ { 2 } - 16 }$

(Multiple Choice)

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Question 313

Find the x- and y-intercepts of f. - $f ( x ) = - x ^ { 2 } ( x + 6 ) \left( x ^ { 2 } - 1 \right)$

(Multiple Choice)

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Question 314

Solve the inequality. - $\frac { x - 2 } { x + 5 } < 0$

(Multiple Choice)

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Question 315

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. - $f ( x ) = 4 ( x - 3 ) ( x + 7 ) ^ { 4 }$

(Multiple Choice)

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Question 316

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis. - $f ( x ) = ( x - 3 ) ^ { 3 }$

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Question 317

Graph the function using transformations. - $f ( x ) = \frac { 1 } { x ^ { 2 } } + 1$ $Graph the function using transformations. - f ( x ) = \frac { 1 } { x ^ { 2 } } + 1 A) B) C) D)$ A) $Graph the function using transformations. - f ( x ) = \frac { 1 } { x ^ { 2 } } + 1 A) B) C) D)$ B) $Graph the function using transformations. - f ( x ) = \frac { 1 } { x ^ { 2 } } + 1 A) B) C) D)$ C) $Graph the function using transformations. - f ( x ) = \frac { 1 } { x ^ { 2 } } + 1 A) B) C) D)$ D) $Graph the function using transformations. - f ( x ) = \frac { 1 } { x ^ { 2 } } + 1 A) B) C) D)$

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Question 318

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 6; zeros: -7, 3, 7 - 5i, -3 + i

(Multiple Choice)

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Question 319

Solve the problem. - $x ^ { 2 } - 36 \leq 0$

(Multiple Choice)

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Question 320

Showing 301 - 320 of 350

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. - $f ( x ) = - 9 x ^ { 4 } + 2 x ^ { 3 } + 8 x + 1 ; [ 1,2 ]$

Find the domain of the rational function. - $f ( x ) = \frac { 8 x } { x - 3 }$

Solve the problem. - $x ^ { 2 } - 3 x \geq - 2$

Solve the problem. - $( b - 2 ) ( b - 3 ) ( b - 4 ) < 0$

Find all zeros of the function and write the polynomial as a product of linear factors. - $f ( x ) = 3 x ^ { 4 } - 7 x ^ { 3 } + 29 x ^ { 2 } - 63 x + 18$

Give the equation of the horizontal asymptote, if any, of the function. - $f ( x ) = \frac { x + 9 } { x ^ { 2 } - 25 }$

Find the vertical asymptotes of the rational function. - $h ( x ) = \frac { x + 11 } { x ^ { 2 } - 16 x }$

Give the equation of the horizontal asymptote, if any, of the function. - $h ( x ) = \frac { 2 x ^ { 3 } - 8 x - 9 } { 7 x + 8 }$

Form a polynomial f(x) with real coefficients having the given degree and zeros. -Degree: 4; zeros: $- 1,2$ , and $1 - 2 \mathrm { i }$ .

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = \sqrt { x } ( \sqrt { x } - 5 )$

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. - $f ( x ) = \left( x + \frac { 1 } { 4 } \right) ^ { 2 } \left( x ^ { 2 } + 7 \right) ^ { 3 }$

Find the vertical asymptotes of the rational function. - $f ( x ) = \frac { x + 2 } { x ^ { 2 } - 16 }$

Find the x- and y-intercepts of f. - $f ( x ) = - x ^ { 2 } ( x + 6 ) \left( x ^ { 2 } - 1 \right)$

Solve the inequality. - $\frac { x - 2 } { x + 5 } < 0$

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. - $f ( x ) = 4 ( x - 3 ) ( x + 7 ) ^ { 4 }$

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis. - $f ( x ) = ( x - 3 ) ^ { 3 }$

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 6; zeros: -7, 3, 7 - 5i, -3 + i

Solve the problem. - $x ^ { 2 } - 36 \leq 0$

Functions and Their Graphs

Linear and Quadratic Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Review

Filters

Exam 3: Polynomial and Rational Functions

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. - f(x)=−9x4+2x3+8x+1;[1,2]f ( x ) = - 9 x ^ { 4 } + 2 x ^ { 3 } + 8 x + 1 ; [ 1,2 ]f(x)=−9x4+2x3+8x+1;[1,2]

Find the domain of the rational function. - f(x)=8xx−3f ( x ) = \frac { 8 x } { x - 3 }f(x)=x−38x​

Solve the problem. - x2−3x≥−2x ^ { 2 } - 3 x \geq - 2x2−3x≥−2

Solve the problem. - (b−2)(b−3)(b−4)<0( b - 2 ) ( b - 3 ) ( b - 4 ) < 0(b−2)(b−3)(b−4)<0

Find all zeros of the function and write the polynomial as a product of linear factors. - f(x)=3x4−7x3+29x2−63x+18f ( x ) = 3 x ^ { 4 } - 7 x ^ { 3 } + 29 x ^ { 2 } - 63 x + 18f(x)=3x4−7x3+29x2−63x+18

Give the equation of the horizontal asymptote, if any, of the function. - f(x)=x+9x2−25f ( x ) = \frac { x + 9 } { x ^ { 2 } - 25 }f(x)=x2−25x+9​

Find the vertical asymptotes of the rational function. - h(x)=x+11x2−16xh ( x ) = \frac { x + 11 } { x ^ { 2 } - 16 x }h(x)=x2−16xx+11​

Give the equation of the horizontal asymptote, if any, of the function. - h(x)=2x3−8x−97x+8h ( x ) = \frac { 2 x ^ { 3 } - 8 x - 9 } { 7 x + 8 }h(x)=7x+82x3−8x−9​

Use transformations of the graph o y=x4 or y=x5y = x ^ { 4 } \text { or } y = x ^ { 5 }y=x4 or y=x5 to graph the function. - f(x)=4−(x−2)5f ( x ) = 4 - ( x - 2 ) ^ { 5 }f(x)=4−(x−2)5 A) B) C) D)

Form a polynomial f(x) with real coefficients having the given degree and zeros. -Degree: 4; zeros: −1,2- 1,2−1,2 , and 1−2i1 - 2 \mathrm { i }1−2i .

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - f(x)=x(x−5)f ( x ) = \sqrt { x } ( \sqrt { x } - 5 )f(x)=x​(x​−5)

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. - f(x)=(x+14)2(x2+7)3f ( x ) = \left( x + \frac { 1 } { 4 } \right) ^ { 2 } \left( x ^ { 2 } + 7 \right) ^ { 3 }f(x)=(x+41​)2(x2+7)3

Find the vertical asymptotes of the rational function. - f(x)=x+2x2−16f ( x ) = \frac { x + 2 } { x ^ { 2 } - 16 }f(x)=x2−16x+2​

Find the x- and y-intercepts of f. - f(x)=−x2(x+6)(x2−1)f ( x ) = - x ^ { 2 } ( x + 6 ) \left( x ^ { 2 } - 1 \right)f(x)=−x2(x+6)(x2−1)

Solve the inequality. - x−2x+5<0\frac { x - 2 } { x + 5 } < 0x+5x−2​<0

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. - f(x)=4(x−3)(x+7)4f ( x ) = 4 ( x - 3 ) ( x + 7 ) ^ { 4 }f(x)=4(x−3)(x+7)4

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis. - f(x)=(x−3)3f ( x ) = ( x - 3 ) ^ { 3 }f(x)=(x−3)3

Graph the function using transformations. - f(x)=1x2+1f ( x ) = \frac { 1 } { x ^ { 2 } } + 1f(x)=x21​+1 A) B) C) D)

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 6; zeros: -7, 3, 7 - 5i, -3 + i

Solve the problem. - x2−36≤0x ^ { 2 } - 36 \leq 0x2−36≤0

Functions and Their Graphs

Linear and Quadratic Functions

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Applications of Trigonometric Functions

Polar Coordinates; Vectors

Analytic Geometry

Systems of Equations and Inequalities

Sequences; Induction; the Binomial Theorem

Counting and Probability

A Preview of Calculus: the Limit, Derivative, and Integral of a Function

Review

Filters

Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the given interval. - $f ( x ) = - 9 x ^ { 4 } + 2 x ^ { 3 } + 8 x + 1 ; [ 1,2 ]$

Find the domain of the rational function. - $f ( x ) = \frac { 8 x } { x - 3 }$

Solve the problem. - $x ^ { 2 } - 3 x \geq - 2$

Solve the problem. - $( b - 2 ) ( b - 3 ) ( b - 4 ) < 0$

Find all zeros of the function and write the polynomial as a product of linear factors. - $f ( x ) = 3 x ^ { 4 } - 7 x ^ { 3 } + 29 x ^ { 2 } - 63 x + 18$

Give the equation of the horizontal asymptote, if any, of the function. - $f ( x ) = \frac { x + 9 } { x ^ { 2 } - 25 }$

Find the vertical asymptotes of the rational function. - $h ( x ) = \frac { x + 11 } { x ^ { 2 } - 16 x }$

Give the equation of the horizontal asymptote, if any, of the function. - $h ( x ) = \frac { 2 x ^ { 3 } - 8 x - 9 } { 7 x + 8 }$

Form a polynomial f(x) with real coefficients having the given degree and zeros. -Degree: 4; zeros: $- 1,2$ , and $1 - 2 \mathrm { i }$ .

State whether the function is a polynomial function or not. If it is, give its degree. If it is not, tell why not. - $f ( x ) = \sqrt { x } ( \sqrt { x } - 5 )$

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. - $f ( x ) = \left( x + \frac { 1 } { 4 } \right) ^ { 2 } \left( x ^ { 2 } + 7 \right) ^ { 3 }$

Find the vertical asymptotes of the rational function. - $f ( x ) = \frac { x + 2 } { x ^ { 2 } - 16 }$

Find the x- and y-intercepts of f. - $f ( x ) = - x ^ { 2 } ( x + 6 ) \left( x ^ { 2 } - 1 \right)$

Solve the inequality. - $\frac { x - 2 } { x + 5 } < 0$

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. - $f ( x ) = 4 ( x - 3 ) ( x + 7 ) ^ { 4 }$

Use the x-intercepts to find the intervals on which the graph of f is above and below the x-axis. - $f ( x ) = ( x - 3 ) ^ { 3 }$

Solve the problem. - $x ^ { 2 } - 36 \leq 0$