Even and Odd Functions Concepts

The video tutorial explores the concepts of even and odd functions, focusing on their symmetry properties. It begins with an introduction to these functions, explaining how even functions have even powers and odd functions have odd powers. The tutorial provides algebraic proofs for even functions and introduces odd functions, encouraging viewers to explore proofs for odd functions independently. Additionally, the video discusses symmetry in trigonometric functions, highlighting sine as an odd function and cosine as an even function, despite not being polynomials.

Why are functions with even powers called even functions?

• Because they are always positive

• Because they have reflection symmetry

• Because they have rotational symmetry

• Because they are always negative

What is the simplest example of an even function?

• x^7

• x^3

• x^2

• x^5

What happens when you substitute -x into an even function?

• The function becomes zero

• The function remains unchanged

• The function doubles

• The function becomes negative

How can you identify an odd function?

• By checking if it has even powers

• By checking if it has odd powers

• By checking if it is always positive

• By checking if it is always negative

What is the algebraic condition for a function to be odd?

• f(x) = f(-x)

• f(x) = -f(-x)

• f(x) = 2f(-x)

• f(x) = 0

Which trigonometric function is an example of an odd function?

• cos(x)

• tan(x)

• sin(x)

• sec(x)

What type of symmetry does the sine function exhibit?

• Rotational symmetry

• Translational symmetry

• Reflection symmetry

• No symmetry

Which trigonometric function is an example of an even function?

• tan(x)

• cot(x)

• cos(x)

• sin(x)

What happens when you reflect the cosine function across the y-axis?

• It becomes a different function

• It remains unchanged

• It becomes zero

• It becomes negative

Why are sine and cosine functions not considered polynomials?

• They are not defined for all x

• They have infinite powers

• They are periodic

• They have no powers