In: Math
For the following exercises, consider the graph of the function f and determine where the function is continuous/ discontinuous and differentiable/not differentiable.
A function is discontinuous wherever there is a point of discontinuity.
A function is not differentiable wherever there is a point of discontinuity or a sharp corner.
Consider the graph provided in the textbook:
The graph of function is continuous on (-∞, -2) ∪ (-2, 0) ∪ (0, ∞).
The graph of function is discontinuous at x = -2 and x = 0.
The graph is differentiable on (-∞, -2) ∪ (-2, -0) ∪ (2, ∞).
The graph of the function is not differentiable at x = -2 because of point of discontinuity.
The graph of the function is not differentiable at x = 0 because of point of discontinuity.
The graph of the function is not differentiable at x = 2 because of a sharp corner.