What are holes in a rational equation?

• A. A point where the function is defined
• B. A value on a graph that can never exist on the function
• C. A discontinuity that cannot be removed
• D. A point where the graph crosses the x-axis

Answer: (B)

A hole comes from a removable discontinuity in a rational function. It shows up at an x-value where both the numerator and denominator are zero, so after simplifying the expression you’d expect a point there, but the original function isn’t defined at that x. Graphically, that x-value would correspond to a point that’s missing from the graph—the y-value is what the simplified form would give, but that specific point isn’t part of the function as written.

So a hole is a value on the graph that cannot exist for the function in its current form. This is why it’s not a point where the function is defined, and why this situation is distinct from a true non-removable discontinuity or a simple x-intercept.