Exam 3: Polynomial and Rational Functions

Find the power function that the graph of f resembles for large values of $| \mathbf { x } |$ - $f ( x ) = - x ^ { 2 } ( x + 4 ) ^ { 3 } \left( x ^ { 2 } - 1 \right)$

(Multiple Choice)

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Question 201

Find the vertical asymptotes of the rational function. - $f ( x ) = \frac { x ( x - 1 ) } { 49 x ^ { 2 } + 84 x + 20 }$

(Multiple Choice)

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Question 202

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. - $f ( x ) = \left( x + \frac { 1 } { 4 } \right) ^ { 4 } ( x + 1 ) ^ { 5 }$

(Multiple Choice)

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Question 203

Solve the problem. - $36 \left( x ^ { 2 } - 1 \right) > 65 x$

(Multiple Choice)

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Question 204

Graph the function. - $f(x)=x+\frac{4}{x}$ $Graph the function. - f(x)=x+\frac{4}{x} A) B) C) D)$ A) $Graph the function. - f(x)=x+\frac{4}{x} A) B) C) D)$ B) $Graph the function. - f(x)=x+\frac{4}{x} A) B) C) D)$ C) $Graph the function. - f(x)=x+\frac{4}{x} A) B) C) D)$ D) $Graph the function. - f(x)=x+\frac{4}{x} A) B) C) D)$

(Multiple Choice)

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Question 205

Use transformations of the graph o $y = x ^ { 4 } \text { or } y = x ^ { 5 }$ to graph the function. - $f ( x ) = - 2 ( x + 3 ) ^ { 5 } + 2$ $Use transformations of the graph o y = x ^ { 4 } \text { or } y = x ^ { 5 } to graph the function. - f ( x ) = - 2 ( x + 3 ) ^ { 5 } + 2 A) B) C) D)$ A) $Use transformations of the graph o y = x ^ { 4 } \text { or } y = x ^ { 5 } to graph the function. - f ( x ) = - 2 ( x + 3 ) ^ { 5 } + 2 A) B) C) D)$ B) $Use transformations of the graph o y = x ^ { 4 } \text { or } y = x ^ { 5 } to graph the function. - f ( x ) = - 2 ( x + 3 ) ^ { 5 } + 2 A) B) C) D)$ C) $Use transformations of the graph o y = x ^ { 4 } \text { or } y = x ^ { 5 } to graph the function. - f ( x ) = - 2 ( x + 3 ) ^ { 5 } + 2 A) B) C) D)$ D) $Use transformations of the graph o y = x ^ { 4 } \text { or } y = x ^ { 5 } to graph the function. - f ( x ) = - 2 ( x + 3 ) ^ { 5 } + 2 A) B) C) D)$

(Multiple Choice)

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Question 206

Find the indicated intercept(s) of the graph of the function.2133:2139 - $f ( x ) = x ^ { 4 } + 12 x ^ { 3 } + 4 x ^ { 2 } + 43 x - 60 ; x + 12$

(Multiple Choice)

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Question 207

Find the domain of the rational function. - $h ( x ) = \frac { x + 2 } { x ^ { 2 } - 36 }$

(Multiple Choice)

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Question 208

Find a bound on the real zeros of the polynomial function. - $f ( x ) = 6 x ^ { 3 } - x ^ { 2 } + 0.3 x - 0.06$

(Multiple Choice)

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Question 209

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. - $f ( x ) = 3 ( x - 6 ) ( x + 7 ) ^ { 3 }$

(Multiple Choice)

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Question 210

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

(Multiple Choice)

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Question 211

Find the domain of the rational function. - $f ( x ) = \frac { 2 x ^ { 2 } - 4 } { 3 x ^ { 2 } + 6 x - 45 }$

(Multiple Choice)

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Question 212

Find the indicated intercept(s) of the graph of the function.2133:2139 - $y$ -intercept of $f ( x ) = \frac { 10 x } { x ^ { 2 } - 19 }$

(Multiple Choice)

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Question 213

Find the indicated intercept(s) of the graph of the function.2133:2139 - $f ( x ) = x ^ { 4 } + 11 x ^ { 3 } + 7 x ^ { 2 } + 71 x - 66 ; x - 11$

(Multiple Choice)

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Question 214

Solve the problem. - $x ^ { 3 } > 4 x ^ { 2 }$

(Multiple Choice)

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Question 215

Find the indicated intercept(s) of the graph of the function.2133:2139 - $y$ -intercept of $f ( x ) = \frac { x } { ( x + 20 ) ( x - 3 ) }$

(Multiple Choice)

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Question 216

Give the equation of the horizontal asymptote, if any, of the function. - $f ( x ) = \frac { - x ^ { 2 } + 16 } { x ^ { 2 } + 5 x + 4 }$

(Multiple Choice)

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Question 217

Find the x- and y-intercepts of f. - $f ( x ) = ( x + 13 ) ^ { 2 }$

(Multiple Choice)

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Question 218

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 6; zeros: $- 2,2 + i , - 1 - i , 0$

(Multiple Choice)

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Question 219

Solve the inequality. - $\frac { ( x - 1 ) ( 3 - x ) } { ( x - 2 ) ^ { 2 } } \leq 0$

(Multiple Choice)

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Question 220

Showing 201 - 220 of 350

Find the power function that the graph of f resembles for large values of $| \mathbf { x } |$ - $f ( x ) = - x ^ { 2 } ( x + 4 ) ^ { 3 } \left( x ^ { 2 } - 1 \right)$

Find the vertical asymptotes of the rational function. - $f ( x ) = \frac { x ( x - 1 ) } { 49 x ^ { 2 } + 84 x + 20 }$

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. - $f ( x ) = \left( x + \frac { 1 } { 4 } \right) ^ { 4 } ( x + 1 ) ^ { 5 }$

Solve the problem. - $36 \left( x ^ { 2 } - 1 \right) > 65 x$

Find the indicated intercept(s) of the graph of the function.2133:2139 - $f ( x ) = x ^ { 4 } + 12 x ^ { 3 } + 4 x ^ { 2 } + 43 x - 60 ; x + 12$

Find the domain of the rational function. - $h ( x ) = \frac { x + 2 } { x ^ { 2 } - 36 }$

Find a bound on the real zeros of the polynomial function. - $f ( x ) = 6 x ^ { 3 } - x ^ { 2 } + 0.3 x - 0.06$

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. - $f ( x ) = 3 ( x - 6 ) ( x + 7 ) ^ { 3 }$

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

Find the domain of the rational function. - $f ( x ) = \frac { 2 x ^ { 2 } - 4 } { 3 x ^ { 2 } + 6 x - 45 }$

Find the indicated intercept(s) of the graph of the function.2133:2139 - $y$ -intercept of $f ( x ) = \frac { 10 x } { x ^ { 2 } - 19 }$

Find the indicated intercept(s) of the graph of the function.2133:2139 - $f ( x ) = x ^ { 4 } + 11 x ^ { 3 } + 7 x ^ { 2 } + 71 x - 66 ; x - 11$

Solve the problem. - $x ^ { 3 } > 4 x ^ { 2 }$

Find the indicated intercept(s) of the graph of the function.2133:2139 - $y$ -intercept of $f ( x ) = \frac { x } { ( x + 20 ) ( x - 3 ) }$

Give the equation of the horizontal asymptote, if any, of the function. - $f ( x ) = \frac { - x ^ { 2 } + 16 } { x ^ { 2 } + 5 x + 4 }$

Find the x- and y-intercepts of f. - $f ( x ) = ( x + 13 ) ^ { 2 }$

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 6; zeros: $- 2,2 + i , - 1 - i , 0$

Solve the inequality. - $\frac { ( x - 1 ) ( 3 - x ) } { ( x - 2 ) ^ { 2 } } \leq 0$

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

Find the power function that the graph of f resembles for large values of ∣x∣| \mathbf { x } |∣x∣ - f(x)=−x2(x+4)3(x2−1)f ( x ) = - x ^ { 2 } ( x + 4 ) ^ { 3 } \left( x ^ { 2 } - 1 \right)f(x)=−x2(x+4)3(x2−1)

Find the vertical asymptotes of the rational function. - f(x)=x(x−1)49x2+84x+20f ( x ) = \frac { x ( x - 1 ) } { 49 x ^ { 2 } + 84 x + 20 }f(x)=49x2+84x+20x(x−1)​

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)4(x+1)5f ( x ) = \left( x + \frac { 1 } { 4 } \right) ^ { 4 } ( x + 1 ) ^ { 5 }f(x)=(x+41​)4(x+1)5

Solve the problem. - 36(x2−1)>65x36 \left( x ^ { 2 } - 1 \right) > 65 x36(x2−1)>65x

Graph the function. - f(x)=x+4xf(x)=x+\frac{4}{x}f(x)=x+x4​ A) B) C) D)

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)=−2(x+3)5+2f ( x ) = - 2 ( x + 3 ) ^ { 5 } + 2f(x)=−2(x+3)5+2 A) B) C) D)

Find the indicated intercept(s) of the graph of the function.2133:2139 - f(x)=x4+12x3+4x2+43x−60;x+12f ( x ) = x ^ { 4 } + 12 x ^ { 3 } + 4 x ^ { 2 } + 43 x - 60 ; x + 12f(x)=x4+12x3+4x2+43x−60;x+12

Find the domain of the rational function. - h(x)=x+2x2−36h ( x ) = \frac { x + 2 } { x ^ { 2 } - 36 }h(x)=x2−36x+2​

Find a bound on the real zeros of the polynomial function. - f(x)=6x3−x2+0.3x−0.06f ( x ) = 6 x ^ { 3 } - x ^ { 2 } + 0.3 x - 0.06f(x)=6x3−x2+0.3x−0.06

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)=3(x−6)(x+7)3f ( x ) = 3 ( x - 6 ) ( x + 7 ) ^ { 3 }f(x)=3(x−6)(x+7)3

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

Find the domain of the rational function. - f(x)=2x2−43x2+6x−45f ( x ) = \frac { 2 x ^ { 2 } - 4 } { 3 x ^ { 2 } + 6 x - 45 }f(x)=3x2+6x−452x2−4​

Find the indicated intercept(s) of the graph of the function.2133:2139 - yyy -intercept of f(x)=10xx2−19f ( x ) = \frac { 10 x } { x ^ { 2 } - 19 }f(x)=x2−1910x​

Find the indicated intercept(s) of the graph of the function.2133:2139 - f(x)=x4+11x3+7x2+71x−66;x−11f ( x ) = x ^ { 4 } + 11 x ^ { 3 } + 7 x ^ { 2 } + 71 x - 66 ; x - 11f(x)=x4+11x3+7x2+71x−66;x−11

Solve the problem. - x3>4x2x ^ { 3 } > 4 x ^ { 2 }x3>4x2

Find the indicated intercept(s) of the graph of the function.2133:2139 - yyy -intercept of f(x)=x(x+20)(x−3)f ( x ) = \frac { x } { ( x + 20 ) ( x - 3 ) }f(x)=(x+20)(x−3)x​

Give the equation of the horizontal asymptote, if any, of the function. - f(x)=−x2+16x2+5x+4f ( x ) = \frac { - x ^ { 2 } + 16 } { x ^ { 2 } + 5 x + 4 }f(x)=x2+5x+4−x2+16​

Find the x- and y-intercepts of f. - f(x)=(x+13)2f ( x ) = ( x + 13 ) ^ { 2 }f(x)=(x+13)2

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 6; zeros: −2,2+i,−1−i,0- 2,2 + i , - 1 - i , 0−2,2+i,−1−i,0

Solve the inequality. - (x−1)(3−x)(x−2)2≤0\frac { ( x - 1 ) ( 3 - x ) } { ( x - 2 ) ^ { 2 } } \leq 0(x−2)2(x−1)(3−x)​≤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

Find the power function that the graph of f resembles for large values of $| \mathbf { x } |$ - $f ( x ) = - x ^ { 2 } ( x + 4 ) ^ { 3 } \left( x ^ { 2 } - 1 \right)$

Find the vertical asymptotes of the rational function. - $f ( x ) = \frac { x ( x - 1 ) } { 49 x ^ { 2 } + 84 x + 20 }$

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. - $f ( x ) = \left( x + \frac { 1 } { 4 } \right) ^ { 4 } ( x + 1 ) ^ { 5 }$

Solve the problem. - $36 \left( x ^ { 2 } - 1 \right) > 65 x$

Find the indicated intercept(s) of the graph of the function.2133:2139 - $f ( x ) = x ^ { 4 } + 12 x ^ { 3 } + 4 x ^ { 2 } + 43 x - 60 ; x + 12$

Find the domain of the rational function. - $h ( x ) = \frac { x + 2 } { x ^ { 2 } - 36 }$

Find a bound on the real zeros of the polynomial function. - $f ( x ) = 6 x ^ { 3 } - x ^ { 2 } + 0.3 x - 0.06$

For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. - $f ( x ) = 3 ( x - 6 ) ( x + 7 ) ^ { 3 }$

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

Find the domain of the rational function. - $f ( x ) = \frac { 2 x ^ { 2 } - 4 } { 3 x ^ { 2 } + 6 x - 45 }$

Find the indicated intercept(s) of the graph of the function.2133:2139 - $y$ -intercept of $f ( x ) = \frac { 10 x } { x ^ { 2 } - 19 }$

Find the indicated intercept(s) of the graph of the function.2133:2139 - $f ( x ) = x ^ { 4 } + 11 x ^ { 3 } + 7 x ^ { 2 } + 71 x - 66 ; x - 11$

Solve the problem. - $x ^ { 3 } > 4 x ^ { 2 }$

Find the indicated intercept(s) of the graph of the function.2133:2139 - $y$ -intercept of $f ( x ) = \frac { x } { ( x + 20 ) ( x - 3 ) }$

Give the equation of the horizontal asymptote, if any, of the function. - $f ( x ) = \frac { - x ^ { 2 } + 16 } { x ^ { 2 } + 5 x + 4 }$

Find the x- and y-intercepts of f. - $f ( x ) = ( x + 13 ) ^ { 2 }$

Information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f. -Degree 6; zeros: $- 2,2 + i , - 1 - i , 0$

Solve the inequality. - $\frac { ( x - 1 ) ( 3 - x ) } { ( x - 2 ) ^ { 2 } } \leq 0$