Exploring Even and Odd Functions in Algebra II

The video tutorial by Kirk Wier on Common Core Algebra 2 covers Unit 7, Lesson 5, focusing on even and odd functions. It explains the definitions of even and odd functions, provides examples, and discusses their graphical representations and symmetries. The tutorial also explores different function types, including cubic and exponential functions, to determine their even or odd properties. The lesson concludes with a summary of the key concepts and their importance in mathematical analysis.

What is the definition of an even function?

• f(x) = -f(x) for all x in the domain

• f(x) = f(-x) for all x in the domain

• f(x) = x^2 for all x in the domain

• f(x) = 0 for all x in the domain

Which of the following is true for an odd function?

• f(x) = f(-x) for all x in the domain

• f(x) = x^3 for all x in the domain

• f(x) = -f(x) for all x in the domain

• f(x) = -f(-x) for all x in the domain

If f(3) = 5 for an even function, what is f(-3)?

• Cannot be determined

• 0

• -5

• 5

For an odd function, if f(7) = -2, what is f(-7)?

• 2

• -2

• 0

• Cannot be determined

What type of symmetry does an even function have?

• Symmetric about the origin

• Symmetric about the y-axis

• No symmetry

• Symmetric about the x-axis

What type of symmetry does an odd function have?

• Symmetric about the origin

• No symmetry

• Symmetric about the y-axis

• Symmetric about the x-axis

Given the function f(x) = |x| - 4, what type of function is it?

• Even

• Odd

• Neither

• Both

For the function g(x) = x^3 - 4x, what type of function is it?

• Even

• Odd

• Neither

• Both

What is the output of f(x) = 2^x for x = -2?

• 1/2

• 4

• 1/4

• 2

Is the function f(x) = 2^x even, odd, or neither?

• Both

• Neither

• Odd

• Even