Exploring Even and Odd Functions

What is the main characteristic of an even function?

• Symmetry with respect to the origin

• Symmetry with respect to the x-axis

• No symmetry

• Symmetry with respect to the y-axis

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

• y = x^3

• y = x^2 + 1

• y = x

• y = |x|

What happens to an even function if its vertex shifts left or right?

• It becomes odd

• It remains even

• It becomes neither even nor odd

• It becomes a linear function

What is the main characteristic of an odd function?

• Symmetry with respect to the x-axis

• Symmetry with respect to the y-axis

• Symmetry with respect to the origin

• No symmetry

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

• y = x^2 + 1

• y = x^2

• y = x^3

• y = |x|

What happens to an odd function if it does not pass through the origin?

• It remains odd

• It becomes even

• It becomes a quadratic function

• It becomes neither even nor odd

How can you algebraically test if a function is even?

• Plug in -x and check if f(-x) = -f(x)

• Plug in x and check if f(x) = f(-x)

• Plug in -x and check if f(-x) = f(x)

• Plug in x and check if f(x) = -f(x)

How can you algebraically test if a function is odd?

• Plug in x and check if f(x) = f(-x)

• Plug in -x and check if f(-x) = f(x)

• Plug in -x and check if f(-x) = -f(x)

• Plug in x and check if f(x) = -f(x)

What is the result of plugging in -x into the function g(x) = x^3 - x?

• x^3 + x

• -x^3 - x

• -x^3 + x

• x^3 - x

What is the classification of the function f(x) = x^3 - 1?

• Odd

• Even

• Both even and odd

• Neither