Exploring Odd and Even Functions

This video tutorial introduces even and odd functions, explaining how to determine them using algebraic and graphical methods. Even functions have symmetry across the y-axis, while odd functions have rotational symmetry about the origin. The video provides examples using x squared and x cubed to illustrate these concepts, demonstrating algebraic proofs for each. The tutorial concludes with a brief mention of further examples available in subsequent videos.

What are the two main methods to determine if a function is even or odd?

• Graphical and statistical methods

• Algebraic and numerical methods

• Numerical and graphical methods

• Algebraic and graphical methods

Which of the following is true for an even function?

• f(x) = x^3

• f(x) = -f(-x)

• f(x) = f(-x)

• f(x) = x^2

What kind of symmetry does the graph of an even function have?

• No symmetry

• Symmetry across the x-axis

• Symmetry across the y-axis

• Rotational symmetry about the origin

In the function f(x) = x^2, what is the result of f(-x)?

• x

• -x

• x^2

• -x^2

What is a characteristic of the exponents in a polynomial function that is even?

• All exponents are even

• Exponents are zero

• All exponents are odd

• Exponents are both even and odd

Which of the following is true for an odd function?

• f(x) = x^3

• f(x) = x^2

• f(x) = -f(-x)

• f(x) = f(-x)

What kind of symmetry does the graph of an odd function have?

• Symmetry across the x-axis

• Symmetry across the y-axis

• Rotational symmetry about the origin

• No symmetry

In the function f(x) = x^3, what is the result of f(-x)?

• -x^3

• x^3

• -x

• x

What is a characteristic of the exponents in a polynomial function that is odd?

• All exponents are even

• Exponents are both even and odd

• All exponents are odd

• Exponents are zero

What happens to the graph of an odd function when it is rotated 180 degrees about the origin?

• It becomes a different graph

• It flips vertically

• It flips horizontally

• It remains unchanged