5.1-5.4 Flashcard Review Rational Functions and Equations

Front

What are asymptotes in rational functions?

Back

Asymptotes are lines that a graph approaches but never touches. They can be vertical, horizontal, or oblique.

Front

How do you find vertical asymptotes?

Back

Vertical asymptotes occur where the denominator of a rational function is zero, provided the numerator is not also zero at that point.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote indicates the value that a function approaches as x approaches infinity or negative infinity.

Front

Simplify the expression: (-17x - 12y) / 15x

Back

(-17x - 12y) / 15x is already in its simplest form.

Front

Simplify the expression: 6x / 20xy

Back

3 / 10y

Front

Simplify the expression: n / 2m

Back

This expression is already in its simplest form.

Front

What does it mean if x varies inversely as y?

Back

It means that as x increases, y decreases, and vice versa, typically expressed as xy = k, where k is a constant.

Front

If x = 3 when y = 8, what is the constant k in the inverse variation?

Back

k = 3 * 8 = 24.

Front

Find y when x = 4 if x varies inversely as y and k = 24.

Back

y = 24 / 4 = 6.

Front

What is the first step in simplifying a rational expression?

Back

Factor both the numerator and the denominator if possible.