Identifying Even, Odd, and Neither Functions

What is the characteristic of the graph of an even function?

• It is not symmetric.

• It has rotational symmetry with respect to the origin.

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

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

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

• x^5

• x

• x^2

• x^3

What is the characteristic of the graph of an odd function?

• It is not symmetric.

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

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

• It has rotational symmetry with respect to the origin.

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

• x^3

• x^6

• x^4

• x^2

What do you need to do to determine if a function is even, odd, or neither using algebra?

• Substitute x with x^3 and compare the result to the original function.

• Substitute x with x^2 and compare the result to the original function.

• Substitute x with 0 and compare the result to the original function.

• Substitute x with -x and compare the result to the original function.

If f(x) = x^2, what type of function is it?

• Cannot be determined

• Neither

• Odd

• Even

If f(x) = x^3, what type of function is it?

• Odd

• Even

• Neither

• Cannot be determined

What does the graph of f(x) = x^2 look like?

• It has rotational symmetry with respect to the origin.

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

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

• It is not symmetric.

What does the graph of f(x) = x^3 look like?

• It has rotational symmetry with respect to the origin.

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

• It is not symmetric.

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

If f(x) = x^3 + x^2 + 1, what type of function is it?

• Even

• Odd

• Neither

• Cannot be determined