Identifying Even and Odd Functions

What is the definition of an even function?

• f(-x) = f(x) for all x in its domain

• f(-x) = -f(x) for all x in its domain

• f(x) = 0 for all x in its domain

• f(x) = x for all x in its domain

What is the symmetry property of even functions?

• Symmetrical with respect to the y-axis

• Symmetrical with respect to the x-axis

• Symmetrical with respect to the origin

• No symmetry

Which of the following is true for an odd function?

• f(-x) = -f(x) for all x in its domain

• f(-x) = f(x) for all x in its domain

• f(x) = x for all x in its domain

• f(x) = 0 for all x in its domain

What is the symmetry property of odd functions?

• Symmetrical with respect to the y-axis

• No symmetry

• Symmetrical with respect to the x-axis

• Symmetrical with respect to the origin

To determine if a function is even, odd, or neither, what should you first calculate?

• f(x)

• f(x) + f(-x)

• f(x) - f(-x)

• f(-x)

If f(x) = x^5 - 2x^3, what is f(-x)?

• x^5 + 2x^3

• -x^5 - 2x^3

• x^5 - 2x^3

• -x^5 + 2x^3

For the function f(x) = x^5 - 2x^3, is it even, odd, or neither?

• Even

• Odd

• Neither

• Both

For the function f(x) = 3x^2 + |x| + 1, is it even, odd, or neither?

• Even

• Odd

• Neither

• Both

For the function f(x) = x^3 + 2x^2 - 1, is it even, odd, or neither?

• Even

• Odd

• Neither

• Both

What does it mean if a function is neither even nor odd?

• It is symmetrical with respect to the y-axis

• It is symmetrical with respect to the origin

• It has no symmetry with respect to the y-axis or the origin

• It is symmetrical with respect to both the y-axis and the origin