Exploring Symmetry in Functions

What is a key characteristic of an even function?

• It has no symmetry.

• It is symmetric about the x-axis.

• It is symmetric about the y-axis.

• It is symmetric about the origin.

Which of the following is an example of an even function?

• f(x) = x^3

• f(x) = x^2

• f(x) = x

• f(x) = x^3 + x

What happens to an odd function when it is flipped over both the y-axis and the x-axis?

• It becomes an even function.

• It becomes a different function.

• It remains the same function.

• It becomes a constant function.

Which of the following is an example of an odd function?

• f(x) = x^6

• f(x) = x^3

• f(x) = x^4

• f(x) = x^2

If f(x) = x^n, when is the function even?

• When n is negative.

• When n is a fraction.

• When n is odd.

• When n is even.

If f(x) = x^n, when is the function odd?

• When n is negative.

• When n is even.

• When n is odd.

• When n is a fraction.

Which of the following functions is neither even nor odd?

• f(x) = x^2

• f(x) = x^4

• f(x) = x^2 + 2

• f(x) = x^3

What happens to the function f(x) = x^2 when it is shifted to the right by 2 units?

• It remains an even function.

• It becomes an odd function.

• It becomes neither even nor odd.

• It becomes a constant function.

What is a unique characteristic of the function f(x) = 0?

• It is only odd.

• It is neither even nor odd.

• It is both even and odd.

• It is only even.

Which of the following statements is true about the function f(x) = 0?

• It changes when flipped over the y-axis.

• It becomes a different function when flipped over both axes.

• It changes when flipped over the x-axis.

• It remains the same when flipped over both axes.