Question

Suppose f (x) is a function defined on all real numbers x. Use the definition of continuity to describe why f is discontinuous at x = a and x = b given the following graphical scenarios.
a) There is a hole in the graph of f at x = a.
b) There is a jump in the graph of f at x = b.

Answer 1

The answer is the same for both lol

Answer 2

a) There exists an epsilon > 0 such that there is no delta such that if |x - a| < delta, then |f(x) - f(a)| < epsilon.
b) There exists an epsilon > 0 such that there is no delta such that if |x - b| < delta, then |f(x) - f(b)| < epsilon.

Answer 3

a) There exists an epsilon > 0 such that there is no delta such that if |x - a| < delta, then |f(x) - f(a)| < epsilon.
b) There exists an epsilon > 0 such that there is no delta such that if |x - b| < delta, then |f(x) - f(b)| < epsilon.

Is that all I need for this?

Answer 4

yep

Answer 5

@tHe_FiZiCx99 lol there's two of you