Identifying Even and Odd Functions

The video tutorial explains how to determine if a function is even, odd, or neither by examining its symmetry. It begins with a discussion on symmetry in graphs, highlighting y-axis and origin symmetry. The tutorial then transitions to algebraic methods for testing symmetry, providing specific tests for even and odd functions. Finally, it demonstrates these tests through examples, showing how to apply them to different functions to determine their symmetry.

What is the main criterion for determining if a function is even, odd, or neither?

• The slope of the function

• The number of roots

• The degree of the polynomial

• The symmetry present in the graph

How can you visually identify an even function on a graph?

• It has a horizontal line of symmetry

• It can be rotated 90 degrees and match up with itself

• It has a vertical line of symmetry

• It can be folded along the y-axis and match up with itself

Which of the following is true for an even function?

• f(-x) = f(x)

• f(-x) = -f(x)

• f(x) = -f(x)

• f(x) = 0

What type of symmetry does an odd function exhibit?

• Symmetry about the y-axis

• Symmetry about the x-axis

• Origin symmetry

• No symmetry

Which of the following is true for an odd function?

• f(x) = -f(x)

• f(x) = 0

• f(-x) = -f(x)

• f(-x) = f(x)

What is the algebraic test for determining if a function is even?

• f(x) = -f(x)

• f(-x) = f(x)

• f(x) = 0

• f(-x) = -f(x)

What is the algebraic test for determining if a function is odd?

• f(x) = 0

• f(-x) = -f(x)

• f(x) = -f(x)

• f(-x) = f(x)

In the first example, why is the function determined to be even?

• Because f(-x) = -f(x)

• Because f(x) = -f(x)

• Because f(-x) = f(x)

• Because f(x) = 0

In the second example, why is the function determined to be neither even nor odd?

• Because f(x) = 0

• Because f(-x) = -f(x)

• Because f(-x) = f(x)

• Because it does not match the original function or its negative

In the third example, why is the function determined to be odd?

• Because it matches the original function with a negative sign

• Because f(x) = 0

• Because f(-x) = f(x)

• Because f(-x) = -f(x)