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Chapter 2: Problem 106

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 function is even, check if its graph is symmetric about the y-axis. For checking if it is odd, observe if it is symmetric about the origin. If the graph isn't symmetric around either, the function is neither even nor odd.

Step by step solution

01

Identify Even Functions

Check if the function graph is symmetric around the y-axis. If it is, the function is said to be an even function. This is based on the mathematical definition: a function is even if and only if for any x and -x in the domain, \(f(x) = f(-x)\). A visual representation of this is symmetry about the y-axis.
02

Identify Odd Functions

Check if the function's graph is symmetric around the origin. If it is, then the function is said to be an odd function. Mathematically speaking, a function is odd if and only if for any x and -x in the domain, \(f(x) = -f(-x)\). A visual representation of this is symmetry about the origin.
03

Identify Neither

If the function's graph is not symmetric about the y-axis or the origin, then the function is neither even nor odd.

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