Unit 4 Review of Rational Funtions

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 an asymptote?

Back

An asymptote is a line that a graph approaches but never touches. It can be vertical, horizontal, 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: 1) If the degree of the numerator is less than the degree of the denominator, the asymptote is y=0. 2) If they are equal, the asymptote is y=\frac{leading coefficient of numerator}{leading coefficient of denominator}. 3) If the degree of the numerator is greater, there is no horizontal asymptote.

Front

What does it mean if a rational function has no horizontal asymptote?

Back

It means that as x approaches infinity or negative infinity, the function's values do not settle towards a constant value.

Front

What is the significance of the degree of a polynomial in rational functions?

Back

The degree of a polynomial determines the end behavior of the rational function and helps in finding asymptotes.

Front

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

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

Front

What is the relationship between the degrees of the numerator and denominator in determining horizontal asymptotes?

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1) If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y=0. 2) If they are equal, the horizontal asymptote is determined by the ratio of the leading coefficients.

Front

What is the vertical asymptote of a rational function?

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A vertical asymptote occurs at values of x that make the denominator zero, provided the numerator is not also zero at those points.

Front

How can you find the vertical asymptotes of a rational function?

Back

To find vertical asymptotes, set the denominator equal to zero and solve for x.

Front

What is the formula for finding the combined work rate of two people working together?

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If person A can complete a task in a minutes and person B in b minutes, their combined work rate is \frac{1}{a} + \frac{1}{b} = \frac{1}{T}, where T is the time taken to complete the task together.