Holes - Point of Discontinuity

Front

What is a vertical asymptote?

Back

A vertical asymptote is a line x = a where a function approaches infinity or negative infinity as the input approaches a. It indicates a point of discontinuity in the function.

Front

How do you find vertical asymptotes in rational functions?

Back

To find vertical asymptotes, set the denominator of the rational function equal to zero and solve for x. The values of x that make the denominator zero are the vertical asymptotes.

Front

What is a hole in a graph of a rational function?

Back

A hole is a point of discontinuity in the graph of a rational function where both the numerator and denominator are zero at the same x-value, indicating that the function is not defined at that point.

Front

How do you identify holes in rational functions?

Back

To identify holes, factor both the numerator and denominator of the rational function. If a common factor exists, the x-value that makes this factor zero is where the hole occurs.

Front

Given f(x) = (x^2 - 9) / (x - 3), what is the vertical asymptote?

Back

x = 3

Front

Given f(x) = (x^2 - 25) / (x - 5), what is the hole?

Back

x = 5

Front

Given f(x) = (x^2 - 121) / (x - 11), what is the hole?

Back

x = 11

Front

Given f(x) = (x^2 - 81) / (x + 9), what is the vertical asymptote?

Back

x = -9

Front

Given f(x) = (x^2 - 64) / (x - 8), what is the hole?

Back

x = 8

Front

What happens to the function at a vertical asymptote?

Back

At a vertical asymptote, the function approaches infinity or negative infinity, indicating that the function does not cross the asymptote.