Problem 121 - Precalculus Essentials

Question

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

Step-by-Step Solution

Answer

The function is even if its graph is symmetric about the y-axis, odd if it's symmetric about the origin, and neither if it doesn't satisfy any of these conditions.

Step 1: Recognize Even Function

Firstly, inspect the given function's graph to see if it is symmetric about the y-axis. If the function fulfils this condition, then it can be classified as an even function. Any point on the graph (x, y) will have a corresponding point (-x, y).

Step 2: Recognize Odd Function

If the function is not even, next check if it's symmetric about the origin. If the function fulfils this condition, then it can be classified as an odd function. For every point (x, y) on the graph, there will be a corresponding point (-x, -y).

Step 3: Classify if Neither

If the function's graph is neither symmetric about the y-axis nor about the origin, then the function is neither even nor odd. It does not satisfy the conditions to be classified as either even or odd.