## How do you tell if a function has a hole or asymptote?

Holes occur when factors from the numerator and the denominator cancel. When a factor in the denominator does not cancel, it produces a vertical asymptote.

**What is the difference between point of discontinuity and vertical asymptote?**

The difference between a “removable discontinuity” and a “vertical asymptote” is that we have a R. discontinuity if the term that makes the denominator of a rational function equal zero for x = a cancels out under the assumption that x is not equal to a. Othewise, if we can’t “cancel” it out, it’s a vertical asymptote.

**How do you know if there is a vertical asymptote?**

Vertical asymptotes can be found by solving the equation n(x) = 0 where n(x) is the denominator of the function ( note: this only applies if the numerator t(x) is not zero for the same x value). Find the asymptotes for the function . The graph has a vertical asymptote with the equation x = 1.

### How do you determine if a function has a vertical asymptote or removable discontinuity?

If a term doesn’t cancel, the discontinuity at this x value corresponding to this term for which the denominator is zero is nonremovable, and the graph has a vertical asymptote. Because the x + 1 cancels, you have a removable discontinuity at x = –1 (you’d see a hole in the graph there, not an asymptote).

**Can a function have a vertical asymptote and a hole?**

More complicated rational functions may have multiple vertical asymptotes. These asymptotes are very important characteristics of the function just like holes. Both holes and vertical asymptotes occur at \begin{align*}x\end{align*} values that make the denominator of the function zero.

**What is the difference between a hole and a point of discontinuity?**

Not quite; if we look really close at x = -1, we see a hole in the graph, called a point of discontinuity. The line just skips over -1, so the line isn’t continuous at that point. It’s not as dramatic a discontinuity as a vertical asymptote, though. In general, we find holes by falling into them.

#### What type of discontinuity is a hole?

removable discontinuity

A removable discontinuity occurs when the graph of a function has a hole.

**Are holes removable discontinuities?**

Removable discontinuities are also known as holes. They occur when factors can be algebraically removed or canceled from rational functions.

**Why do holes occur in rational functions?**

HoleA hole exists on the graph of a rational function at any input value that causes both the numerator and denominator of the function to be equal to zero. They occur when factors can be algebraically canceled from rational functions.

## Do holes Trump asymptotes?

We’ll say it again, since it’s important: Vertical asymptotes occur at roots (a.k.a. zeros) of the denominator after the rational function has been simplified; holes occur at roots of the denominator that cancel out entirely during the simplification.

**How do you find a horizontal asymptote?**

The location of the horizontal asymptote is determined by looking at the degrees of the numerator (n) and denominator (m). If n horizontal asymptote. If n=m, then y=an / bm is the horizontal asymptote. That is, the ratio of the leading coefficients.

**How to find a horizontal asymptote?**

Put equation or function in y= form.

### When is there a horizontal asymptote?

When n is much less than m,the horizontal asymptote is y = zero or the x -axis.

**What are horizontal asymptotes?**

A horizontal asymptote is a y-value on a graph which a function approaches but does not actually reach. Here is a simple graphical example where the graphed function approaches, but never quite reaches, y=0.