Vertical asymptotes

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line that a graph approaches but never touches or crosses. It occurs where the function's value becomes infinite.

Front

How do you find vertical asymptotes in a rational function?

Back

Vertical asymptotes are found by setting the denominator of a rational function equal to zero and solving for x.

Front

What is the significance of vertical asymptotes in graphing?

Back

Vertical asymptotes indicate values of x where the function is undefined and help in understanding the behavior of the graph near those points.

Front

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

Back

It implies that as x approaches 3, the function's value approaches infinity or negative infinity.

Front

Back

The vertical asymptotes are at x = 3 and x = -3, found by setting the denominator x^2 - 9 = 0.

Front

Which asymptote(s) are determined by looking at the denominator?

Back

Vertical asymptotes are determined by looking at the denominator of a rational function.

Front

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

Back

The graph will approach the vertical asymptote but will never touch or cross it.

Front

Can a function have more than one vertical asymptote?

Back

Yes, a function can have multiple vertical asymptotes depending on the factors in the denominator.

Front

What is the relationship between vertical asymptotes and limits?

Back

As x approaches a vertical asymptote, the limit of the function approaches infinity or negative infinity.

Front

How do you determine if a vertical asymptote exists at a certain x-value?

Back

A vertical asymptote exists at x = a if the limit of the function approaches infinity as x approaches a.