If the graph of a function is symmetric about the y-axis, which of the following

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Question: If the graph of a function is symmetric about the y-axis, which of the following types of functions could it be?

Options:

Correct Answer: Even function

Solution:

A function is symmetric about the y-axis if it is an even function, which satisfies the condition f(x) = f(-x).

If the graph of a function is symmetric about the y-axis, which of the following types of functions could it be?

If the graph of a function is symmetric about the y-axis, which of the following types of functions could it be?

Step 1: Understand what symmetry about the y-axis means. This means that if you fold the graph along the y-axis, both sides will match perfectly.
Step 2: Learn about even functions. An even function is defined by the property that f(x) = f(-x) for all x in its domain.
Step 3: Recognize that if a function is even, its graph will be symmetric about the y-axis.
Step 4: Conclude that if a function's graph is symmetric about the y-axis, it must be an even function.

Even Functions – A function is even if it satisfies the condition f(x) = f(-x), indicating symmetry about the y-axis.