Algebraic Even Odd or Neither Functions

The video tutorial explains the concepts of even and odd functions, focusing on their symmetries about the Y-axis and the origin, respectively. It covers both algebraic and graphical methods to determine if a function is even or odd. The tutorial provides examples using quadratic and cubic functions, demonstrating how to evaluate symmetry algebraically by substituting negative inputs. The video concludes with a practical application using Desmos to visualize these concepts.

What is the symmetry property of even functions?

• Symmetrical about the X-axis

• Symmetrical about the Y-axis

• Symmetrical about the origin

• No symmetry

How can you algebraically determine if a function is odd?

• Plug in negative X and get the opposite of the function

• Plug in positive X and get the same function

• Plug in negative X and get the same function

• Plug in positive X and get the opposite of the function

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

• x^3

• -x^3

• x^2

• -x^2

What is the result of plugging in negative X for the function G(x) = 2/x^2 - 5?

• 2/x^2 + 5

• -2/x^2 - 5

• -2/x^2 + 5

• 2/x^2 - 5

Which of the following functions is neither even nor odd?

• f(x) = 2/x^2 - 5

• f(x) = x^3 - x^2 + 7

• f(x) = x^3

• f(x) = x^2

What does the graph of an odd function look like?

• Symmetrical about the X-axis

• Symmetrical about the origin

• No symmetry

• Symmetrical about the Y-axis

In the Desmos graph, what happens when you plug in -2 for an odd function?

• You get zero

• You get the same value as plugging in 2

• You get a positive value

• You get the opposite value of plugging in 2