Find the numbers, if any, where the function $f ( x ) = \left\{ \begin{array} { c l } 3 x - 2 & \text { if } x \leq 1 \ 0 & \text { if } x 1 \end{array} \right.$ is discontinuous.
A) $- 2$
B) 2
C) 1
D) 0

Question

Find the numbers, if any, where the function $f ( x ) = \left\{ \begin{array} { c l } 3 x - 2 & \text { if } x \leq 1 \ 0 & \text { if } x > 1 \end{array} \right.$ is discontinuous.
A) $- 2$
B) 2
C) 1
D) 0

Quizplus · Accepted Answer

The function is defined piecewise. Therefore, we need to check the continuity at the boundary of each piece. • Continuity at x = 1: lim_(x→1^-) f(x) = 3(1) - 2 = 1 lim_(x→1^+) f(x) = 0 Since the left and right limits are not equal at x = 1, the function is discontinuous at x = 1. • Continuity at x < 1: The function is given by f(x) = 3x - 2, which is a polynomial function. Polynomials are continuous everywhere, therefore the function is continuous for x < 1. • Continuity at x > 1: The function is given by f(x) = 0, which is a constant function. Constant functions are also continuous everywhere, therefore the function is continuous for x > 1. Overall, the only point where the function is discontinuous is x = 1.

Find the Numbers, If Any, Where the Function f(x)={3x−2 if x≤10 if x>1f ( x ) = \left\{ \begin{array} { c l } 3 x - 2 & \text { if } x \leq 1 \\ 0 & \text { if } x > 1 \end{array} \right.f(x)={3x−20​ if x≤1 if x>1​

Find the Numbers, If Any, Where the Function $f ( x ) = \left\{ \begin{array} { c l } 3 x - 2 & \text { if } x \leq 1 \\ 0 & \text { if } x > 1 \end{array} \right.$