Use the definition of continuity, lim(x->a)f(x)=f(a), to show that the following are continuous or discontinuous.

Question

(A): f(x)= {3x x≤2}

{x² x>2}

(B): f(x)= {x³ x≤2}

{4+2x x>2}

Answer 1

A is discontinuous and B is continuous.

All polynomials are continuous everywhere. That makes the question of continuity only an issue at the point

x=2. In the first question, the left and right limits are unequal; therefore not continuous.