Exploring Even and Odd Functions

What is the main difference between even and odd functions?

• Even functions are negated when reflected about the x-axis, while odd functions are unchanged when reflected about the y-axis.

• Even functions are unchanged when reflected about the y-axis, while odd functions are negated when reflected about the y-axis.

• Even functions are unchanged when reflected about the x-axis, while odd functions are unchanged when reflected about the y-axis.

• Even functions are unchanged when reflected about the origin, while odd functions are negated when reflected about the origin.

What happens to an even function when you plug in -x?

• The function becomes undefined.

• The function remains the same.

• The function is negated.

• The function becomes zero.

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

• It has no symmetry.

• It is negated when reflected about the x-axis.

• It is unchanged when reflected about the y-axis.

• It can be rotated 180 degrees about the origin.

What happens to an odd function when you plug in -x?

• The function becomes zero.

• The function remains the same.

• The function becomes undefined.

• The function is negated.

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

• It can be rotated 180 degrees about the origin.

• It is unchanged when reflected about the y-axis.

• It has no symmetry.

• It is negated when reflected about the x-axis.

How can you identify a function that is neither even nor odd?

• It has symmetry about the y-axis.

• It has rotational symmetry about the origin.

• It has no symmetry about the y-axis or the origin.

• It is unchanged when reflected about the x-axis.

What is the degree of a polynomial if its end behavior goes in opposite directions?

• Even degree

• Undefined degree

• Odd degree

• Neither even nor odd degree

What must an odd function pass through to have rotational symmetry?

• The x-axis

• None of the above

• The y-axis

• The origin

If a function has symmetry about the y-axis, what type of function is it?

• Odd function

• Undefined function

• Even function

• Neither even nor odd function

What is the degree and type of a polynomial if its end behavior is in opposite directions and it has rotational symmetry about the origin?

• Even degree and even function

• Odd degree and odd function

• Even degree and odd function

• Odd degree and even function