Exploring Even and Odd Functions

What is the defining property of an even function?

• f(-x) = -f(x)

• f(-x) = f(x)

• f(x) = -f(x)

• f(x) = x^2

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

• y = x^3 + 1

• y = x^3

• y = x^2 + 1

• y = x^2

What does it mean for a graph to have y-axis symmetry?

• The graph is not symmetric

• The graph is symmetric about the y-axis

• The graph is symmetric about the x-axis

• The graph is symmetric about the origin

What is the defining property of an odd function?

• f(x) = x^2

• f(x) = -f(x)

• f(-x) = f(x)

• f(-x) = -f(x)

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

• y = x^2

• y = x^2 + 1

• y = x^3 + 1

• y = x^3

What type of symmetry does an odd function have?

• Origin symmetry

• No symmetry

• x-axis symmetry

• y-axis symmetry

What happens when you cube a negative number?

• You get a positive result

• You get a negative result

• The result is undefined

• The result is zero

What is the result of f(-x) for the function f(x) = x^3 + 1?

• x^3 + 1

• x^3 - 1

• -x^3 + 1

• -x^3 - 1

Can a function be neither even nor odd?

• Only if it is a polynomial

• No

• Only if it is a trigonometric function

• Yes

What is the opposite of the function f(x) = x^3 + 1?

• x^3 - 1

• -x^3 + 1

• -x^3 - 1

• x^3 + 1