Question

If h is a piecewise linear function and limx→ah(x) does not exist, what could represent the function h?

a) A continuous function
b) A vertical asymptote at x=a
c) A jump discontinuity at x=a
d) A horizontal asymptote at x=a

Answer 1

The function h represents a jump discontinuity at x=a.

Step-by-step explanation:

The function h represents a jump discontinuity at x=a.

A jump discontinuity occurs when there is a sudden change in the value of the function at a specific value of x. In this case, the limit of h(x) as x approaches a does not exist because h(x) takes on different values from the left and right of a.

For example, if h(x) = 2 for x < a and h(x) = 4 for x > a, the function h would have a jump discontinuity at x=a.