Table of Contents
What does holes mean in math?
Vocabulary
| Term | Definition |
|---|---|
| Hole | A 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. |
| Rational Function | A rational function is any function that can be written as the ratio of two polynomial functions. |
How do you find asymptotes and holes?
Set each factor in the denominator equal to zero and solve for the variable. If this factor does not appear in the numerator, then it is a vertical asymptote of the equation. If it does appear in the numerator, then it is a hole in the equation.
Why are there holes in rational functions?
The holes in a rational function are the result of it sharing common factors shared by the numerator and denominator. These are coordinates that the function passes through but are not part of the function’s domain and range.
Is a hole a circle?
A circle in the plane can be continuously shrunk to a point,* but intuitively, and in the sense of homotopy and homology, a circle has a hole in it. (For our purposes, a one-dimensional sphere is a circle, a two-dimensional sphere is basketball-shaped, and so on.
Whats considered a hole?
noun. an opening through something; gap; aperture: a hole in the roof; a hole in my sock. a hollow place in a solid body or mass; a cavity: a hole in the ground.
Is a hole the same as a vertical asymptote?
Earlier, you were asked how asymptotes are different than holes. 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. Both holes and vertical asymptotes restrict the domain of a rational function.
How do you show holes in Desmos?
Click on the graph either to the left or to the right of the removable discontinuity (hole). Drag toward the removable discontinuity to find the limit as you approach the hole.
Is undefined a hole?
The limit at a hole: The limit at a hole is the height of the hole. is undefined, the result would be a hole in the function. Function holes often come about from the impossibility of dividing zero by zero.