Question

Which functions have removable discontinuities (holes)?

1) Polynomial functions
2) Rational functions
3) Exponential functions
4) Trigonometric functions

Answer 1

Removable discontinuities or holes occur in rational functions when a factor in the denominator cancels out with a factor in the numerator.

Step-by-step explanation:

Rational functions have removable discontinuities or holes. Removable discontinuities or holes occur in rational functions when a factor in the denominator cancels out with a factor in the numerator. These occur when a factor in the denominator cancels out with a factor in the numerator, resulting in a hole in the graph. For example, the rational function f(x) = (x^2 - 4)/(x - 2) has a removable discontinuity at x = 2, where the factor (x - 2) cancels out.

Polynomial functions, exponential functions, and trigonometric functions do not have removable discontinuities. Polynomial functions can have other types of discontinuities such as jumps or vertical asymptotes. Exponential functions and trigonometric functions are continuous throughout their domains.