Rational Functions

Front

What are asymptotes?

Back

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

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

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

Back

y = 2

Front

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

Back

y = 0

Front

How do you find vertical asymptotes?

Back

Vertical asymptotes occur where the function is undefined, typically where the denominator equals zero.

Front

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

Back

x = 2

Front

What is the simplified form of √4√12?

Back

4√3

Front

What is the horizontal asymptote of the function f(x) = 5x^2 + 3x / 2x^2 + 1?

Back

y = 5/2

Front

What is the significance of horizontal asymptotes in rational functions?

Back

Horizontal asymptotes indicate the behavior of the function as x approaches infinity or negative infinity.

Front

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

Back

x = 2 and x = -2