Mathematics

Problem

Let

g(x)=\begin{cases}3, & x<2\\5, & x\ge 2\end{cases}

Which statement best describes the discontinuity of

g

x=2

? a) No discontinuity;

g

is continuous at

x=2

because

g(2)

exists. b) Removable discontinuity, because redefining

g(2)

could make the limits match. c) Jump discontinuity, because the one-sided limits are finite but unequal. d) Infinite discontinuity, because the function "jumps" so the limit is unbounded near

x=2

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