Exploring Even and Odd Functions in Algebra 2

This video tutorial covers Algebra 2 Unit 7 Lesson 5 on even and odd functions. It begins with an introduction to functions and their classifications, followed by formal definitions of even and odd functions. The tutorial explains these concepts graphically and provides examples and exercises for better understanding. It analyzes absolute value functions and explores cubic polynomials, discussing their properties and classifications. The video concludes with a discussion on exponential functions, encouraging students to explore their classification further.

Which of the following is NOT a type of function mentioned in the introduction?

• Linear function

• Exponential function

• Logarithmic function

• Quadratic function

A function is considered even if:

• F(x) = -F(x)

• F(-x) = -F(x)

• F(-x) = F(x)

• F(x) = F(-x)

What is the defining characteristic of an odd function?

• F(x) = F(-x)

• F(-x) = F(x)

• F(x) = -F(x)

• F(-x) = -F(x)

In an even function, opposite inputs give:

• Undefined outputs

• Zero outputs

• The same outputs

• Opposite outputs

For an odd function, if the input is 3 and the output is 5, what is the output for the input -3?

• 5

• -5

• 0

• Undefined

What type of symmetry does an even function exhibit?

• Symmetry about the x-axis

• Symmetry about the y-axis

• Symmetry about the origin

• No symmetry

Which of the following functions is likely to be even?

• f(x) = x^3 - 4x

• f(x) = |x| - 4

• f(x) = 2^x

• f(x) = x^2 + 3

What is the output of the function f(x) = |x| - 4 for the input -7?

• 3

• -7

• -3

• 7

What type of function is f(x) = x^3 - 4x?

• Neither

• Odd

• Even

• Both

What is the symmetry of the function f(x) = 2^x?

• Symmetric about the y-axis

• Symmetric about the x-axis

• Symmetric about the origin

• Neither even nor odd