In Problem use the graph of y = f(x) in Figure 9.40 to find the functional values and limits, if they exist.

The given graph represents the function f(x).

(a)

We need to find the value of f(4). It means, we have to find the value of the given function at x=4.

From the given graph it is clear that the function has an open circle and a closed circle x=4.

An open circle means that the point is not included in the function and a closed circle means that the point is included in the function.

We have a closed circle at point (4,2). So, the value of the given function is 2 at x=4. Thus,

$f\left(4\right)=2$

(b)

We need to find the value of $\underset{x\to 4^{-}}{\lim }f\left(x\right)$. It means, we have to find the left-hand limit of the given function at x=4.

From the given function, it is clear that the function approaches towards 1 as x approaches to 4 from the left.

So, the left-hand limit of the given function at x=4 is 1. It can be written as

$\underset{x\to 4^{-}}{\lim }f\left(x\right)=1$