Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 1 - Limits and Their Properties - 1.2 Exercises - Page 56: 27

Answer

See the attached image.

Work Step by Step

There are many possible ways to draw the graph. See the attached image for a sample. To satisfy the requirements, first note that f(2) = 6,which means we can draw a closed circle at x=2 for the value 6. But the limit as the graph approaches 2 is 3, so we can create a discontinuity at x=2 for the value 3. The function can have any shape as it approaches x=2 as long as its values from the left and right both approach 3. Then we know that f(0) is undefined, but the limit as x approaches 0 is 4. So we can create an open circle at x=0 for the value 4. Again, the function can have any shape as it approaches x=0 as long as its values from the left and right both approach 4.
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