Exploring Even and Odd Functions

This lesson covers the identification and characteristics of even and odd functions, focusing on their graphical representations and symmetry. It explains how to graph polynomial functions, describes the symmetry of these graphs, and distinguishes between even and odd functions based on their exponents. The lesson also discusses the behavior of functions as they approach infinity and provides examples to illustrate these concepts. Students are encouraged to use symmetry to determine function types and are given homework instructions for further practice.

What is the primary goal of lesson 3.3?

• To recognize and distinguish even and odd functions

• To learn about linear functions

• To study trigonometric functions

• To understand quadratic equations

What type of graph does the function f(x) = 3x^2 + 1 represent?

• A cubic curve

• A straight line

• A parabola

• A hyperbola

How does the graph of f(x) = 2x^3 + 3x behave?

• It forms a circle

• It forms a cubic curve with a sideways S shape

• It forms a straight line

• It forms a parabola

What type of symmetry does the graph of f(x) = 3x^2 + 1 exhibit?

• Symmetry about the y-axis

• Symmetry about the x-axis

• Rotational symmetry

• No symmetry

What type of symmetry does the graph of f(x) = 2x^3 + 3x exhibit?

• Symmetry about the x-axis

• Rotational symmetry around the origin

• Symmetry about the y-axis

• No symmetry

What is a characteristic of all even functions?

• They have no symmetry

• They have symmetry over the y-axis

• They have symmetry around the origin

• They have only odd powers of x

What is a characteristic of all odd functions?

• They have only even powers of x

• They have symmetry over the y-axis

• They have symmetry around the origin

• They have no symmetry

Why is the function f(x) = 4x^2 + 8x neither even nor odd?

• Because it has both even and odd exponents

• Because it has only even exponents

• Because it has only odd exponents

• Because it has no exponents

What happens to the graph of a polynomial function as x approaches negative infinity and positive infinity if it is an odd function?

• The graph forms a circle

• The graph forms a parabola

• Both ends go in opposite directions

• Both ends go in the same direction

What is the signature move of an odd function?

• The graph forms a straight line

• Both ends of the graph go in opposite directions

• Both ends of the graph go in the same direction

• The graph has no symmetry