Determining Even and Odd Functions

What is the main characteristic of an even function when viewed graphically?

• Symmetrical about the y-axis

• Symmetrical about the origin

• No symmetry

• Symmetrical about the x-axis

Which of the following is true for odd functions when viewed graphically?

• They are symmetrical about the y-axis

• They are symmetrical about the x-axis

• They are symmetrical about the origin

• They have no symmetry

What is the graphical characteristic of a function that is neither even nor odd?

• No symmetry

• Symmetrical about the origin

• Symmetrical about the x-axis

• Symmetrical about the y-axis

What is the algebraic test for determining if a function is even?

• Plug in f(x) and check if it equals -f(x)

• Plug in -x and check if it equals f(x)

• Plug in x and check if it equals -f(x)

• Plug in -x and check if it equals -f(x)

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

• -x

• x^2

• -x^2

• x

What is the algebraic test for determining if a function is odd?

• Plug in x and check if it equals -f(x)

• Plug in -x and check if it equals -f(x)

• Plug in -x and check if it equals f(x)

• Plug in f(x) and check if it equals -f(x)

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

• x^3

• -x^3

• -x

• x

What happens if you plug in -x into a function and get neither f(x) nor -f(x)?

• The function is odd

• The function is even

• The function is both even and odd

• The function is neither even nor odd

Which of the following is true for a function that is neither even nor odd?

• It is symmetrical about the y-axis

• It is symmetrical about the x-axis

• It has no symmetry

• It is symmetrical about the origin

What is the key takeaway for determining if a function is even, odd, or neither?

• Neither graphical nor algebraic methods are reliable

• Both graphical and algebraic methods can be used

• Only algebraic methods should be used

• Only graphical methods should be used