Exam 3: Polynomial and Rational Functions

Find an nth degree polynomial function with real coefficients satisfying the given conditions. - $\mathrm { n } = 3 ; - 1$ and $3 + 2 \mathrm { i }$ are zeros; leading coefficient is 1

(Multiple Choice)

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Question 401

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. - $17 x ^ { 2 } - 3 x \leq 0$ $Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. - 17 x ^ { 2 } - 3 x \leq 0$

(Multiple Choice)

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Question 402

Find the domain of the rational function. - $f ( x ) = \frac { x + 7 } { x ^ { 2 } - 4 x }$

(Multiple Choice)

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Question 403

Find the x-intercepts (if any) for the graph of the quadratic function. - $7 x ^ { 2 } + 8 x + 2 = 0$ Give your answers in exact form.

(Multiple Choice)

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Question 404

Solve the problem. -A drug is injected into a patient and the concentration of the drug is monitored. The drug's concentration, $C ( t )$ , in milligrams after $t$ hours is modeled by $C ( t ) = \frac { 5 t } { 3 t ^ { 2 } + 1 } \text {. }$ What is the horizontal asymptote for this function? Describe what this means in practical terms.

(Multiple Choice)

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Question 405

Choose the one alternative that best completes the statement or answers the question. Use the vertex and intercepts to sketch the graph of the quadratic function. -f $(x)=-2 x^{2}+20 x-49$ $Choose the one alternative that best completes the statement or answers the question. Use the vertex and intercepts to sketch the graph of the quadratic function. -f (x)=-2 x^{2}+20 x-49$

(Multiple Choice)

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Question 406

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - $f ( x ) = \left( x + \frac { 1 } { 5 } \right) ^ { 2 } ( x + 3 ) ^ { 3 }$

(Multiple Choice)

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Question 407

Find the indicated intercept(s) of the graph of the function. -Is there $y$ -axis symmetry for the rational function $f ( x ) = \frac { - 5 x ^ { 2 } - 5 x - 9 } { - 2 x + 16 }$ ?

(Multiple Choice)

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Question 408

Solve the problem. -The revenue achieved by selling $x$ graphing calculators is figured to be $x ( 21 - 0.2 x )$ dollars. The cost of each calculator is $\$ 13$ . How many graphing calculators must be sold to make a profit (revenue - cost) of at least $\$ 72.80$ ?

(Multiple Choice)

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Question 409

Find the vertical asymptotes, if any, of the graph of the rational function. - $g ( x ) = \frac { x } { x ^ { 2 } - 25 }$

(Multiple Choice)

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Question 410

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. - $f ( x ) = - x ^ { 2 } ( x + 2 ) \left( x ^ { 2 } - 1 \right)$

(Multiple Choice)

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Question 411

Solve the problem. -A drug is injected into a patient and the concentration of the drug is monitored. The drug's concentrati $C ( t )$ , in milligrams per liter after $t$ hours is modeled by $C ( t ) = \frac { 5 t } { 3 t ^ { 2 } + 4 } \text {. }$ Estimate the drug's concentration after 5 hours. (Round to the nearest hundredth.)

(Multiple Choice)

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Question 412

Determine the constant of variation for the stated condition. -The voltage across a resistor is jointly proportional to the resistance of the resistor and the current flowing through the resistor. If the voltage across a resistor is 32 volts for a resistor whose resistance is 4 ohms and when the current flowing through the resistor is 8 amperes, find the voltage across a resistor whose resistance is 2 ohms and when the current flowing through the resistor is 7 amperes.

(Multiple Choice)

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Question 413

Find the horizontal asymptote, if any, of the graph of the rational function. - $g ( x ) = \frac { 4 x ^ { 2 } - 9 x - 5 } { 8 x ^ { 2 } - 3 x + 5 }$

(Multiple Choice)

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Question 414

Solve the problem. -Use synthetic division to divide $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 19 x + 30$ by $x - 6$ . Use the result to find all zeros of $f$ .

(Multiple Choice)

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Question 415

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. -Touches the $x$ -axis at 0 and crosses the $x$ -axis at 4 ; lies above the $x$ -axis between 0 and 4 .

(Multiple Choice)

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Question 416

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. - $x ^ { 2 } + 12 x + 35 > 0$ $Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. - x ^ { 2 } + 12 x + 35 > 0$

(Multiple Choice)

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Question 417

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } + 5$

(Multiple Choice)

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Question 418

Find the x-intercepts (if any) for the graph of the quadratic function. - $f ( x ) = - x ^ { 2 } + 17 x - 72$

(Multiple Choice)

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Question 419

Divide using synthetic division. - $\left( x ^ { 5 } - 3 x ^ { 4 } - 5 x ^ { 3 } + x ^ { 2 } - x + 40 \right) \div ( x + 2 )$

(Multiple Choice)

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Question 420

Showing 401 - 420 of 532

Find an nth degree polynomial function with real coefficients satisfying the given conditions. - $\mathrm { n } = 3 ; - 1$ and $3 + 2 \mathrm { i }$ are zeros; leading coefficient is 1

Find the domain of the rational function. - $f ( x ) = \frac { x + 7 } { x ^ { 2 } - 4 x }$

Find the x-intercepts (if any) for the graph of the quadratic function. - $7 x ^ { 2 } + 8 x + 2 = 0$ Give your answers in exact form.

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - $f ( x ) = \left( x + \frac { 1 } { 5 } \right) ^ { 2 } ( x + 3 ) ^ { 3 }$

Find the indicated intercept(s) of the graph of the function. -Is there $y$ -axis symmetry for the rational function $f ( x ) = \frac { - 5 x ^ { 2 } - 5 x - 9 } { - 2 x + 16 }$ ?

Solve the problem. -The revenue achieved by selling $x$ graphing calculators is figured to be $x ( 21 - 0.2 x )$ dollars. The cost of each calculator is $\$ 13$ . How many graphing calculators must be sold to make a profit (revenue - cost) of at least $\$ 72.80$ ?

Find the vertical asymptotes, if any, of the graph of the rational function. - $g ( x ) = \frac { x } { x ^ { 2 } - 25 }$

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. - $f ( x ) = - x ^ { 2 } ( x + 2 ) \left( x ^ { 2 } - 1 \right)$

Find the horizontal asymptote, if any, of the graph of the rational function. - $g ( x ) = \frac { 4 x ^ { 2 } - 9 x - 5 } { 8 x ^ { 2 } - 3 x + 5 }$

Solve the problem. -Use synthetic division to divide $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 19 x + 30$ by $x - 6$ . Use the result to find all zeros of $f$ .

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. -Touches the $x$ -axis at 0 and crosses the $x$ -axis at 4 ; lies above the $x$ -axis between 0 and 4 .

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } + 5$

Find the x-intercepts (if any) for the graph of the quadratic function. - $f ( x ) = - x ^ { 2 } + 17 x - 72$

Divide using synthetic division. - $\left( x ^ { 5 } - 3 x ^ { 4 } - 5 x ^ { 3 } + x ^ { 2 } - x + 40 \right) \div ( x + 2 )$

Equations and Inequalities

Functions and Graphs

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections and Analytic Geometry

Sequences, Induction, and Probability

Prerequisites: Fundamental Concepts of Algebra

Filters

Exam 3: Polynomial and Rational Functions

Find an nth degree polynomial function with real coefficients satisfying the given conditions. - n=3;−1\mathrm { n } = 3 ; - 1n=3;−1 and 3+2i3 + 2 \mathrm { i }3+2i are zeros; leading coefficient is 1

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. - 17x2−3x≤017 x ^ { 2 } - 3 x \leq 017x2−3x≤0

Find the domain of the rational function. - f(x)=x+7x2−4xf ( x ) = \frac { x + 7 } { x ^ { 2 } - 4 x }f(x)=x2−4xx+7​

Find the x-intercepts (if any) for the graph of the quadratic function. - 7x2+8x+2=07 x ^ { 2 } + 8 x + 2 = 07x2+8x+2=0 Give your answers in exact form.

Choose the one alternative that best completes the statement or answers the question. Use the vertex and intercepts to sketch the graph of the quadratic function. -f (x)=−2x2+20x−49(x)=-2 x^{2}+20 x-49(x)=−2x2+20x−49

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - f(x)=(x+15)2(x+3)3f ( x ) = \left( x + \frac { 1 } { 5 } \right) ^ { 2 } ( x + 3 ) ^ { 3 }f(x)=(x+51​)2(x+3)3

Find the indicated intercept(s) of the graph of the function. -Is there yyy -axis symmetry for the rational function f(x)=−5x2−5x−9−2x+16f ( x ) = \frac { - 5 x ^ { 2 } - 5 x - 9 } { - 2 x + 16 }f(x)=−2x+16−5x2−5x−9​ ?

Find the vertical asymptotes, if any, of the graph of the rational function. - g(x)=xx2−25g ( x ) = \frac { x } { x ^ { 2 } - 25 }g(x)=x2−25x​

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. - f(x)=−x2(x+2)(x2−1)f ( x ) = - x ^ { 2 } ( x + 2 ) \left( x ^ { 2 } - 1 \right)f(x)=−x2(x+2)(x2−1)

Find the horizontal asymptote, if any, of the graph of the rational function. - g(x)=4x2−9x−58x2−3x+5g ( x ) = \frac { 4 x ^ { 2 } - 9 x - 5 } { 8 x ^ { 2 } - 3 x + 5 }g(x)=8x2−3x+54x2−9x−5​

Solve the problem. -Use synthetic division to divide f(x)=x3−10x2+19x+30f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 19 x + 30f(x)=x3−10x2+19x+30 by x−6x - 6x−6 . Use the result to find all zeros of fff .

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. -Touches the xxx -axis at 0 and crosses the xxx -axis at 4 ; lies above the xxx -axis between 0 and 4 .

Solve the polynomial inequality and graph the solution set on a number line. Express the solution set in interval notation. - x2+12x+35>0x ^ { 2 } + 12 x + 35 > 0x2+12x+35>0

Find the axis of symmetry of the parabola defined by the given quadratic function. - f(x)=x2+5f ( x ) = x ^ { 2 } + 5f(x)=x2+5

Find the x-intercepts (if any) for the graph of the quadratic function. - f(x)=−x2+17x−72f ( x ) = - x ^ { 2 } + 17 x - 72f(x)=−x2+17x−72

Divide using synthetic division. - (x5−3x4−5x3+x2−x+40)÷(x+2)\left( x ^ { 5 } - 3 x ^ { 4 } - 5 x ^ { 3 } + x ^ { 2 } - x + 40 \right) \div ( x + 2 )(x5−3x4−5x3+x2−x+40)÷(x+2)

Equations and Inequalities

Functions and Graphs

Exponential and Logarithmic Functions

Trigonometric Functions

Analytic Trigonometry

Additional Topics in Trigonometry

Systems of Equations and Inequalities

Matrices and Determinants

Conic Sections and Analytic Geometry

Sequences, Induction, and Probability

Prerequisites: Fundamental Concepts of Algebra

Filters

Find an nth degree polynomial function with real coefficients satisfying the given conditions. - $\mathrm { n } = 3 ; - 1$ and $3 + 2 \mathrm { i }$ are zeros; leading coefficient is 1

Find the domain of the rational function. - $f ( x ) = \frac { x + 7 } { x ^ { 2 } - 4 x }$

Find the x-intercepts (if any) for the graph of the quadratic function. - $7 x ^ { 2 } + 8 x + 2 = 0$ Give your answers in exact form.

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. - $f ( x ) = \left( x + \frac { 1 } { 5 } \right) ^ { 2 } ( x + 3 ) ^ { 3 }$

Find the indicated intercept(s) of the graph of the function. -Is there $y$ -axis symmetry for the rational function $f ( x ) = \frac { - 5 x ^ { 2 } - 5 x - 9 } { - 2 x + 16 }$ ?

Find the vertical asymptotes, if any, of the graph of the rational function. - $g ( x ) = \frac { x } { x ^ { 2 } - 25 }$

Find the x-intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. - $f ( x ) = - x ^ { 2 } ( x + 2 ) \left( x ^ { 2 } - 1 \right)$

Find the horizontal asymptote, if any, of the graph of the rational function. - $g ( x ) = \frac { 4 x ^ { 2 } - 9 x - 5 } { 8 x ^ { 2 } - 3 x + 5 }$

Solve the problem. -Use synthetic division to divide $f ( x ) = x ^ { 3 } - 10 x ^ { 2 } + 19 x + 30$ by $x - 6$ . Use the result to find all zeros of $f$ .

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. -Touches the $x$ -axis at 0 and crosses the $x$ -axis at 4 ; lies above the $x$ -axis between 0 and 4 .

Find the axis of symmetry of the parabola defined by the given quadratic function. - $f ( x ) = x ^ { 2 } + 5$

Find the x-intercepts (if any) for the graph of the quadratic function. - $f ( x ) = - x ^ { 2 } + 17 x - 72$

Divide using synthetic division. - $\left( x ^ { 5 } - 3 x ^ { 4 } - 5 x ^ { 3 } + x ^ { 2 } - x + 40 \right) \div ( x + 2 )$