Question

Describe the continuity of the graphed function

Answer 1

we know that

Any function f(x) is continuous at x=a only if

$\lim_{x \to a-} f(x) = \lim_{x \to a+} f(x)=f(a)$

We can see that this curve is smooth everywhere except at x=3

so, we will check continuity at x=3

Left limit is:

$\lim_{x \to 3-} f(x) = 0$

Right limit is:

$\lim_{x \to 3+} f(x) = 0$

Functional value:

$f(3)= 3$

we can see that all three values are not equal

so, this function is discontinuous at x=3

Since, limit exists and function value is defined only they are not equal

so, there will be removal discontinuity at x=3

so, option-B........Answer