Understanding Even and Odd Functions

What characteristic helps in visually identifying an even function?

• Symmetry around the origin

• Symmetry around the y-axis

• Symmetry around the x-axis

• No symmetry

Which of the following is a property of even functions?

• f(x) = x^2

• f(x) = 0

• f(x) = -f(-x)

• f(x) = f(-x)

What happens to the function value when you reflect an even function over the y-axis?

• It halves

• It becomes negative

• It remains the same

• It doubles

How can you visually recognize an odd function?

• No symmetry

• Symmetry around the origin

• Symmetry around the x-axis

• Symmetry around the y-axis

What is the formal definition of an odd function?

• f(x) = x^2

• f(x) = -f(-x)

• f(x) = 0

• f(x) = f(-x)

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

• f(x) = x^2

• f(x) = x^3

• f(x) = x^5

• f(x) = x^4

What is the result of reflecting an odd function over both the x and y axes?

• It remains unchanged

• It becomes an even function

• It becomes a constant function

• It becomes a different odd function

Which of the following functions is neither even nor odd?

• f(x) = x^2

• f(x) = 0

• f(x) = x^3

• f(x) = x^3 + 1

Which function property indicates that it is neither even nor odd?

• f(x) = -f(-x)

• f(x) = 0

• f(x) = f(-x)

• f(x) = x^3 + 1

What is a common misconception about shifted cubic functions?

• They are even functions

• They are odd functions

• They are neither even nor odd

• They are constant functions