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