What are even and odd functions

The video tutorial explains the concepts of even and odd functions, focusing on their symmetry properties. Even functions are symmetrical about the Y-axis, while odd functions are symmetrical about the origin. The tutorial provides examples and tests to illustrate these properties, emphasizing that not all functions with even exponents are even functions, and similarly for odd functions.

What is the main characteristic of an even function in terms of symmetry?

• Symmetrical about the Y-axis

• Symmetrical about the X-axis

• Symmetrical about the origin

• Not symmetrical

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

• f(x) = x^3 - x^2

• f(x) = x^3

• f(x) = x^2 + x

• f(x) = x^2

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

• f(-x) = -f(x)

• f(x) = f(-x)

• f(-x) = f(x)

• f(x) = -f(x)

What is the main characteristic of an odd function in terms of symmetry?

• Symmetrical about the X-axis

• Not symmetrical

• Symmetrical about the Y-axis

• Symmetrical about the origin

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

• f(x) = x^2

• f(x) = x^3 - x^2

• f(x) = x^2 + x

• f(x) = x^3

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

• f(-x) = f(x)

• f(x) = -f(x)

• f(x) = f(-x)

• f(-x) = -f(x)

If f(x) = x^3 - x^2, is this function odd?

• No, because f(-x) does not equal -f(x)

• Yes, because it is symmetrical about the Y-axis

• No, because f(-x) = f(x)

• Yes, because f(-x) = -f(x)