Horizontal and Vertical Asymptotes

Front

What is a horizontal asymptote?

Back

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

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line that the graph of a function approaches as the input (x) approaches a specific value where the function is undefined.

Front

How do you find horizontal asymptotes for rational functions?

Back

To find horizontal asymptotes of a rational function, compare the degrees of the numerator and denominator. If the degree of the numerator is less, the asymptote is y=0. If they are equal, the asymptote is y = leading coefficient of numerator / leading coefficient of denominator.

Front

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

Back

The vertical asymptote is x = 2.

Front

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

Back

The horizontal asymptote is y = 3/2.

Front

If a function has a vertical asymptote at x = -3, what does this imply about the function?

Back

It implies that the function approaches infinity or negative infinity as x approaches -3.

Front

What happens to the graph of a function at a vertical asymptote?

Back

The graph of the function will increase or decrease without bound (approach infinity or negative infinity) as it gets close to the vertical asymptote.

Front

Can a function have more than one vertical asymptote?

Back

Yes, a function can have multiple vertical asymptotes depending on the values that make the denominator zero.

Front

What is the significance of horizontal asymptotes in graphing functions?

Back

Horizontal asymptotes indicate the behavior of the function as x approaches infinity or negative infinity, helping to understand the end behavior of the graph.

Front

How do you determine the vertical asymptotes of a rational function?

Back

Set the denominator equal to zero and solve for x. The solutions are the equations of the vertical asymptotes.