Question

A real function \[f\] is a continuous function when it is continuous at which points?

Options

• Only every integer in its domain

• Only the points where \[f(c)=0\]

• Every point in its domain

• Only the left endpoint of its domain

Answer 1

A continuous function is continuous at every point in its domain. Equivalently, \[\lim_{x\to c}f(x)=f(c)\] for every \[c\] in the domain of \[f\].