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

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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In Problem use the graph of y = f(x) in Figure 9.40 to find the functional values and limits, if they exist.

 

Expert Solution
Step 1

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(4)=2

Step 2

(b)

We need to find the value of limx4-f(x). 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

limx4-f(x)=1

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