y Continuous on [a, b) y5 f(x) Right- continuous at a a (a) Continuous on (a, b] y 5 g(x) Left- continuous at b a (b)
y Continuous on [a, b) y5 f(x) Right- continuous at a a (a) Continuous on (a, b] y 5 g(x) Left- continuous at b a (b)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
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Question
Modify the graphs of the functions ƒ and g as shown to obtain functions that are continuous on 3a, b4.
Expert Solution
Step 1
Given that the graph of functions and are given.
We have to modify the graphs of the functions and to obtain functions that are continuous on .
Step 2
Continuous of a function:
If a function is continuous at , then .
Continuous for the graph :
At the left endpoint,
The graph is defined at and .
Thus, the graph is right continuous at .
At the right endpoint,
The graph is undefined at and exits.
To make is left continuous at , we can define .
Answer:
To modify the graph at for , such that the graph is continuous on the interval .
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