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5. Rational Functions

Introduction to Rational Functions

5. Rational Functions

Introduction to Rational Functions

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Finding the Domain of Rational Functions

Finding the Domain of Rational Functions

Finding the Domain of Rational Functions

Finding the Domain of Rational Functions

Finding the Domain of Rational Functions

Finding the Domain of Rational Functions

Rational Expressions and Domain

Rational Expressions and Domain

Finding the Domain of a Rational Function / Fraction with Variable in Denominator

Finding the Domain of a Rational Function / Fraction with Variable in Denominator

Finding the Domain of an Expression Involving Fractions - Example 1

Finding the Domain of an Expression Involving Fractions - Example 1

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Practice this topic

Multiple Choice

Find the domain of the rational function. Then, write it in lowest terms.

$f\left(x\right)=\frac{x^2+9}{x-3}$

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Multiple Choice

Find the domain of the rational function. Then, write it in lowest terms.

$f\left(x\right)=\frac{6x^5}{2x^2-8}$

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Textbook Question

Provide a short answer to each question. What is the domain of the function ƒ(x)=1/x? What is its range?

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Textbook Question

Provide a short answer to each question. Is ƒ(x)=1/x^2 an even or an odd function? What symmetry does its graph exhibit?

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Textbook Question

In Exercises 1–8, find the domain of each rational function. f(x)=(x+7)/(x^2+49)

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Textbook Question

Use the graph of the rational function in the figure shown to complete each statement in Exercises 15–20.

As x -> -2^+, f(x) -> __

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Textbook Question

In Exercises 21–36, find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of each rational function. f(x)=x/(x+4)

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Textbook Question

Match the rational function in Column I with the appropriate descrip-tion in Column II. Choices in Column II can be used only once. ƒ(x)=(x^2-16)/(x+4)

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Textbook Question

In Exercises 21–36, find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of each rational function. r(x)=(x^2+4x−21)/(x+7)

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Textbook Question

In Exercises 37–44, find the horizontal asymptote, if there is one, of the graph of each rational function. f(x)=12x/(3x^2+1)

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Textbook Question

Give the equations of any vertical, horizontal, or oblique asymptotes for the graph of each rational function. See Example 4. ƒ(x)=(x^2+1)/(x^2+9)

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Textbook Question

In Exercises 45–56, use transformations of f(x)=1/x or f(x)=1/x^2 to graph each rational function. h(x)=1/x2 − 4

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Textbook Question

In Exercises 55–56, use transformations of f(x) = (1/x) or f(x) = (1/x^2) to graph each rational function. g(x) = 1/(x + 2)^2 - 1

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Textbook Question

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

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Textbook Question

In Exercises 57–80, follow the seven steps to graph each rational function. f(x)=(3x^2+x−4)/(2x^2−5x)

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Textbook Question

In Exercises 95–98, use long division to rewrite the equation for g in the form quotient + remainder/divisor. Then use this form of the function's equation and transformations of f(x) = 1/x to graph g. g(x) = (2x+7)/(x+3)

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