A function f is defined as follows: f(x) = {(0 for x < 0),(x for 0 ≤ x < 1),(-x^2 + 4x - 2 for 1 ≤ x < 3), (4 - x for x ≥ 3)

Question

A function f is defined as follows:

\(f(x) = \begin{cases} 0 & \quad \text{for } x<0 \text{ }\\ x & \quad \text{for }0≤x<1 \text{ }\\ -x^2+4x-2& \quad \text{for }1≤x<3 \text{ }\\ 4-x& \quad \text{for }x≥3 \text{ } \end{cases}\)

Is the function continuous?

Answer 1

From (i), (ii) and (iii) 

f(x) is continuous at x = 0, 1, 3