Rational Functions & Asymptotes

Front

What occurs when a factor in the denominator cancels with a factor in the numerator of a rational function?

Back

A hole in the rational function.

Front

Where are the holes in the rational function if the function is defined as f(x) = (x+4)(x-2)/(x+4)?

Back

x = -4.

Front

What is the horizontal asymptote of a rational function?

Back

The horizontal line that the graph approaches as x approaches infinity.

Front

What is the horizontal asymptote for the function f(x) = (2x^2 + 3)/(x^2 + 1)?

Back

y = 2.

Front

What are asymptotes in the context of rational functions?

Back

Lines that the graph approaches but never touches.

Front

What are the vertical asymptotes of the function f(x) = 1/(x-6)?

Back

x = 6.

Front

How do you find vertical asymptotes in a rational function?

Back

Set the denominator equal to zero and solve for x.

Front

What is the significance of horizontal asymptotes in rational functions?

Back

They indicate the end behavior of the function as x approaches infinity or negative infinity.

Front

What is the vertical asymptote for the function f(x) = 1/(x^2 - 4)?

Back

x = 2 and x = -2.

Front

What does it mean if a rational function has a hole?

Back

It means there is a point where the function is not defined due to a canceled factor.