Can there be a hole at x 0?

Now if the Numerator and the Denominator of the Rational expression are both Zero (0), for the same value of x, then the Division by Zero at this value of x is said to be ‘meaningless’ or undetermined, and we have a Hole in the Graph at this Value of x.

How do you find the hole in a graph?

Before putting the rational function into lowest terms, factor the numerator and denominator. If there is the same factor in the numerator and denominator, there is a hole. Set this factor equal to zero and solve. The solution is the x-value of the hole.

How do you know if a limit does not exist on a graph?

Limits & Graphs Here are the rules: If the graph has a gap at the x value c, then the two-sided limit at that point will not exist. If the graph has a vertical asymptote and one side of the asymptote goes toward infinity and the other goes toward negative infinity, then the limit does not exist.

What does a hole in a graph mean?

rational function
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. Removable discontinuityRemovable discontinuities are also known as holes.

How do you tell if a vertical asymptote has a hole?

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.

What are holes in a graph?

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. Removable discontinuityRemovable discontinuities are also known as holes.

How do you find a hole in a graph on 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.

How do you find the discontinuity of an equation?

Start by factoring the numerator and denominator of the function. A point of discontinuity occurs when a number is both a zero of the numerator and denominator. Since is a zero for both the numerator and denominator, there is a point of discontinuity there. To find the value, plug in into the final simplified equation.