Rational Functions

Front

What is a rational function?

Back

A rational function is a function that can be expressed as the quotient of two polynomials, typically in the form f(x) = P(x)/Q(x), where P and Q are polynomials and Q(x) ≠ 0.

Front

What is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches. It can be horizontal, vertical, or oblique.

Front

How do you find the horizontal asymptote of a rational function?

Back

To find the horizontal asymptote, compare the degrees of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, y=0 is the horizontal asymptote. If they are equal, divide the leading coefficients.

Front

What is the x-intercept of a function?

Back

The x-intercept is the point where the graph of the function crosses the x-axis, found by setting f(x) = 0 and solving for x.

Front

What is the vertical asymptote of a rational function?

Back

The vertical asymptote occurs where the denominator of the rational function is equal to zero, provided that the numerator is not also zero at that point.

Front

How do you determine the x-intercept of a rational function?

Back

To find the x-intercept, set the numerator equal to zero and solve for x.

Front

What is the significance of the leading coefficient in a rational function?

Back

The leading coefficient affects the end behavior of the function as x approaches positive or negative infinity.

Front

What is the domain of a rational function?

Back

The domain of a rational function is all real numbers except where the denominator equals zero.

Front

How do you find the equation of a vertical asymptote?

Back

Set the denominator of the rational function equal to zero and solve for x.

Front

What does the graph of a rational function typically look like?

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The graph of a rational function can have one or more asymptotes, and it may have breaks or holes where the function is undefined.