Exploring Even and Odd Functions

What does it mean for a function to be symmetric with respect to the y-axis?

• It is neither even nor odd.

• It is symmetric with respect to the origin.

• It is an even function.

• It is an odd function.

Which of the following is true for an even function?

• f(x) = -f(-x)

• f(x) = -f(x)

• f(x) = f(-x)

• f(x) = x^2

If a function is even, what should be true about its graph?

• It should be symmetric with respect to the origin.

• It should be symmetric with respect to the y-axis.

• It should be symmetric with respect to the x-axis.

• It should have no symmetry.

What happens when you evaluate an even function at -x?

• You get the opposite value of f(x).

• You get the same value as f(x).

• You get a negative value.

• You get zero.

Which of the following is a characteristic of an odd function?

• It is symmetric with respect to the y-axis.

• It is symmetric with respect to the origin.

• It is symmetric with respect to the x-axis.

• It has no symmetry.

What does a 180-degree rotation about the origin indicate about a function?

• The function is even.

• The function is odd.

• The function is neither even nor odd.

• The function is symmetric with respect to the y-axis.

For an odd function, what should be true about the y-intercept?

• It must pass through the origin.

• It must be negative.

• It can be any value.

• It must be positive.

What is the algebraic test for an odd function?

• f(x) = -f(x)

• f(x) = -f(-x)

• f(x) = x^2

• f(x) = f(-x)

If a function is odd, what should be true about its graph?

• It should be symmetric with respect to the x-axis.

• It should be symmetric with respect to the origin.

• It should have no symmetry.

• It should be symmetric with respect to the y-axis.

How can you determine if a function is even, odd, or neither using a data table?

• By checking if f(x) = f(-x) for all x.

• By checking if f(x) = -f(-x) for all x.

• By checking if f(x) = -f(x) for all x.

• By checking if f(x) = x^2 for all x.