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Rational Function Analysis

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Questions and Answers

What are the x-intercepts of the rational function f(x)?

The x-intercepts occur where the function f(x) equals zero, which is found by setting the numerator equal to zero.

How do you determine the y-intercept of the function f(x)?

The y-intercept can be found by evaluating f(0), which requires substituting x = 0 into the function.

What is the equation of the horizontal asymptote for the function f(x)?

The horizontal asymptote can be determined by analyzing the degrees of the numerator and denominator of f(x).

Explain how to find the vertical asymptotes of the rational function f(x).

<p>Vertical asymptotes are found by setting the denominator equal to zero and solving for x.</p> Signup and view all the answers

Describe the process for determining the domain of the function f(x).

<p>The domain consists of all real numbers except where the denominator equals zero.</p> Signup and view all the answers

Flashcards

X-Intercepts of a Rational Function

The x-values where the graph of a function crosses the x-axis. To find them, set the function equal to zero and solve for x.

Y-Intercept of a Rational Function

The y-value where the graph of a function crosses the y-axis. To find it, set x equal to zero and evaluate the function.

Horizontal Asymptote

A horizontal line the graph of a function approaches as x approaches positive or negative infinity. To find it, compare the degrees of the numerator and denominator.

Vertical Asymptotes

Vertical lines that the graph of a function approaches as x approaches a certain value. To find them, set the denominator of the function equal to zero and solve for x.

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Domain of a Rational Function

The set of all possible x-values for which the function is defined. For rational functions, exclude any x-values that make the denominator zero.

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Study Notes

Rational Function Analysis

Function: f(x) = (unspecified rational expression)
x-intercepts: Find the x values where f(x) = 0. (Need the function f(x) to determine the values.)
y-intercept: Find the y value when x = 0. (Need the function f(x) to determine the value.)
Horizontal Asymptote: Determine the equation of the horizontal asymptote. (Need the function f(x) to determine the equation.)
Vertical Asymptotes: Find the vertical asymptotes. (Need the function f(x) to determine the equation(s)).
Domain: Identify the values of x for which the function is defined. (Need the function f(x) to determine the domain.)
Graph: Graph the function, including the x-intercepts, y-intercept, asymptotes, and any crucial points. (Requires the function f(x) to produce an accurate graph.)

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Description

Explore the key features of rational functions in this quiz. You'll analyze x-intercepts, y-intercepts, asymptotes, and the domain of a given rational function. Dive in to enhance your understanding of function behavior and graphing techniques.