Identifying Even and Odd Functions from Tables

The video tutorial explores the properties of functions, specifically focusing on determining whether a function is even, odd, or neither. It begins with an introduction to function f and its properties, followed by definitions of even and odd functions. The tutorial then provides examples to illustrate each type: an even function, a function that is neither even nor odd, and an odd function. Through these examples, the video demonstrates how to analyze functions using symmetry and algebraic properties.

What is the definition of an even function?

• f(x) = x

• f(x) = f(-x)

• f(x) = -f(x)

• f(x) = -f(-x)

What is the definition of an odd function?

• f(x) = f(-x)

• f(x) = -f(x)

• f(x) = -f(-x)

• f(x) = x

In the first example, what is f(7) equal to?

• -2

• 2

• -1

• 1

In the first example, what is f(-3) equal to?

• 2

• -1

• 1

• -2

In the second example, what is f(-5) equal to?

• -2

• 2

• 1

• 0

Why is the function in the second example neither even nor odd?

• Because f(-5) is equal to 2

• Because f(5) is equal to -f(5)

• Because f(5) is equal to f(-5)

• Because f(-5) is not equal to f(5) or -f(5)

In the third example, what is f(-4) equal to?

• -8

• 8

• 0

• 4

In the third example, what is f(-1) equal to?

• 1

• 0

• -5

• 5

Why is the function in the third example considered odd?

• Because f(x) is equal to x

• Because f(-x) is equal to -f(x)

• Because f(x) is equal to -f(x)

• Because f(-x) is equal to f(x)

What is f(0) equal to in the third example?

• 5

• -1

• 1

• 0