Which equation holds for an even function?

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Study for the NBCT Mathematics AYA Component 1 exam. Utilize flashcards and multiple-choice questions with detailed explanations for each question. Prepare efficiently for success in your teaching certification journey!

Multiple Choice

Which equation holds for an even function?

Explanation:
Even functions are symmetric about the y-axis, so their value at x matches the value at -x. This gives the condition f(-x) = f(x) for every x in the domain, which is just another way of writing f(x) = f(-x). That symmetry about the y-axis is what makes a function even. The other forms describe different ideas: f(-x) = -f(x) is the odd-function condition, reflecting symmetry about the origin; f(x) = -f(-x) is just another way to express the odd property; and f(-x) = f(x) - 1 would break the even symmetry in general, since the outputs at x and -x wouldn’t match.

Even functions are symmetric about the y-axis, so their value at x matches the value at -x. This gives the condition f(-x) = f(x) for every x in the domain, which is just another way of writing f(x) = f(-x). That symmetry about the y-axis is what makes a function even.

The other forms describe different ideas: f(-x) = -f(x) is the odd-function condition, reflecting symmetry about the origin; f(x) = -f(-x) is just another way to express the odd property; and f(-x) = f(x) - 1 would break the even symmetry in general, since the outputs at x and -x wouldn’t match.

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