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Chapter 8: Q. 3 (page 669)

Fill in the blanks: The graph of every odd function is symmetric about ______. The graph of every even function is symmetric about ______.

Short Answer

Expert verified

On filling up the blanks, we get, "The graph of every odd function is symmetric about the origin. The graph of every even function is symmetric about the y-axis."

Step by step solution

01

Step 1. Explanation of the functions.

A function f is an odd function if f(−x)=−f(x) for all x in the domain of f.

A function f is an even function iff(−x)=f(x)for all x in the domain of f.

02

Step 2. Explain the graph of the functions.

The graph of an odd function has symmetry with respect to the origin, which means its graph remains unchanged after rotation of 180degrees about the origin.

The graph of an even function is symmetric with respect to the y-axis, which means its graph remains unchanged after reflection about the y-axis.

On completing the sentence, we get, "The graph of every odd function is symmetric about the origin. The graph of every even function is symmetric about the y-axis."

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Most popular questions from this chapter

In Exercises 23–32 we ask you to give Lagrange’s form for the corresponding remainder, R4(x)

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where p is a nonnegative integer, arises in many applications in physics and engineering, including one model for the vibration of a beaten drum. The solution of the differential equation is called the Bessel function of order p, denoted by Jp(x). It may be shown that Jp(x) is given by the following power series in x:

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Graph the first four terms in the sequence of partial sums of J1(x).

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