Identifying Even and Odd Functions

This video tutorial by Mark Heredos on MathGuide.com explores even and odd functions. It begins with definitions of even and odd functions, explaining their properties and how they can be identified visually and algebraically. The video uses examples to illustrate symmetry in functions and provides a step-by-step guide on using algebra to determine if a function is even or odd. The tutorial also includes visual examples using graphs and discusses trigonometric functions.

What is the defining characteristic of an even function?

• f(x) = -f(x)

• f(x) = x^3

• f(x) = f(-x)

• f(x) = x^2

If f(-3) = f(3) for a function f(x), what type of function is it?

• Linear

• Even

• Neither

• Odd

What is the defining characteristic of an odd function?

• f(x) = -f(-x)

• f(x) = f(-x)

• f(x) = -f(x)

• f(x) = x^2

If f(-2) = -f(2) for a function f(x), what type of function is it?

• Neither

• Odd

• Quadratic

• Even

What type of symmetry does an even function have?

• No symmetry

• Symmetry with respect to the x-axis

• Symmetry with respect to the y-axis

• Symmetry with respect to the origin

What type of symmetry does an odd function have?

• Symmetry with respect to the y-axis

• Symmetry with respect to the x-axis

• No symmetry

• Symmetry with respect to the origin

Is the function y = x^3 even, odd, or neither?

• Neither

• Odd

• Even

• Both

Is the function y = x^2 + 1 even, odd, or neither?

• Neither

• Odd

• Even

• Both

What is the result of substituting -x into an even function?

• The function becomes undefined

• The function becomes zero

• The function becomes its negative

• The function remains the same

What is the result of substituting -x into an odd function?

• The function remains the same

• The function becomes its negative

• The function becomes undefined

• The function becomes zero