Sketch the graph of an example of a function f that satisfies all of the given conditions....

Question:

Sketch the graph of an example of a function {eq}f {/eq} that satisfies all of the given conditions.

{eq}\lim_{x \rightarrow 0^-} f(x) = 2\\ \lim_{x \rightarrow 0^+} f(x) = 0\\ \lim_{x \rightarrow 4^-} f(x) = 3\\ \lim_{x \rightarrow 4^+} f(x) = 0\\ f(0) = 2\\ f(4) = 1 {/eq}

One-Sided Limits of the Function

We will sketch a function {eq}f {/eq}, in which the arrangement of limes is important, not its monotony, concavity, etc. Notice that we will denote with an arrow if we observe one-sided limits and with a point if it is a function value.

In case a one-sided limit is equal to the function value at the same point that we are observing, it is the case where the function is defined so the arrow is unnecessary.

Answer and Explanation:


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Using a Graph to Define Limits

from Math 104: Calculus

Chapter 6 / Lesson 1
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