If the graph of a function f(x) is symmetric about the y-axis, which of the foll

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Question: If the graph of a function f(x) is symmetric about the y-axis, which of the following must be true?

Options:

Correct Answer: f(x) = f(-x) for all x.

Solution:

A function that is symmetric about the y-axis satisfies the property f(x) = f(-x) for all x.

If the graph of a function f(x) is symmetric about the y-axis, which of the following must be true?

If the graph of a function f(x) is symmetric about the y-axis, which of the following must be true?

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: Recognize that for a function to be symmetric about the y-axis, the output (y-value) for a positive input (x) must be the same as the output for the negative of that input (-x).
Step 3: Write down the property that describes this symmetry: f(x) = f(-x). This means that for every x, the function value at x is equal to the function value at -x.
Step 4: Conclude that if a function is symmetric about the y-axis, it must satisfy the property f(x) = f(-x) for all values of x.

Even Functions – A function is even if it is symmetric about the y-axis, which means it satisfies the condition f(x) = f(-x) for all x.