Vertical asymptotes

Front

What is a vertical asymptote?

Back

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

Front

How do you find vertical asymptotes in a rational function?

Back

To find vertical asymptotes, set the denominator of the rational function equal to zero and solve for x.

Front

What does it mean if a function has no vertical asymptotes?

Back

If a function has no vertical asymptotes, it means that the function does not approach infinity for any value of x in its domain.

Front

If a function has vertical asymptotes at x = 2 and x = -3, what does this indicate?

Back

This indicates that as x approaches 2 or -3, the function's value approaches infinity or negative infinity.

Front

What is the relationship between vertical asymptotes and the domain of a function?

Back

Vertical asymptotes indicate values that are excluded from the domain of the function, as the function is undefined at these points.

Front

How many vertical asymptotes can a rational function have?

Back

A rational function can have one or more vertical asymptotes, depending on the degree of the polynomial in the denominator.

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Back

The vertical asymptote is at x = 3.

Front

Back

The vertical asymptotes are at x = -2 and x = 5.

Front

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

Back

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

Front

Can vertical asymptotes occur in functions other than rational functions?

Back

Yes, vertical asymptotes can also occur in some logarithmic and trigonometric functions.