Solving 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, where the denominator is not zero.

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 vertical asymptotes of a rational function?

Back

Vertical asymptotes occur at the values of x that make the denominator zero, provided the numerator is not also zero at those points.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Front

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

Back

1. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. 2. If the degrees are equal, the horizontal asymptote is y = leading coefficient of numerator / leading coefficient of denominator. 3. If the degree of the numerator is greater, there is no horizontal asymptote.

Front

What is the process for solving a rational equation?

Back

1. Identify the rational expressions. 2. Find a common denominator. 3. Multiply both sides by the common denominator to eliminate fractions. 4. Solve the resulting equation.

Front

What does it mean to simplify a rational expression?

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To simplify a rational expression means to reduce it to its lowest terms by canceling common factors in the numerator and denominator.

Front

What is a hole in a rational function?

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A hole occurs in the graph of a rational function at x-values that make both the numerator and denominator zero, indicating a removable discontinuity.

Front

How do you find the x-intercepts of a rational function?

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The x-intercepts are found by setting the numerator equal to zero and solving for x.

Front

What is the significance of the y-intercept in a rational function?

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The y-intercept is the value of the function when x = 0, found by evaluating the function at x = 0.