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Chapter 2: Problem 103

If you are given a function's graph, how do you determine if the function is even, odd, or neither?

Short Answer

Expert verified
To determine if a graph represents an even, odd, or neither function, check for symmetry. If the graph is symmetrical about the y-axis, it's even. If it's symmetrical about the origin, it's odd. If it's not symmetrical about either the y-axis or the origin, it's neither.

Step by step solution

01

Identify symmetrical properties

First, inspect the graph visually to identify its symmetrical properties.
02

Check for symmetry about the y-axis

Examine whether the function is symmetrical about the y-axis. This means the left and right halves of the graph are mirror images of each other. If this is the case, it's an even function.
03

Check for symmetry about the origin

Examine whether the function is symmetrical about the origin. In this case, the graph in the second quadrant is a reflection of the graph in the fourth quadrant across the y-axis, and the graph in the third quadrant is a reflection of the graph in the first quadrant across the y-axis. If this is true, the function is odd.
04

Check for no symmetry

If the function's graph is neither symmetrical about the y-axis nor about the origin, then the function is neither even nor odd.

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