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)

Tags

CCSS.HSF.BF.B.3

What is the definition of an odd function?

• f(x) = f(-x)

• f(x) = -f(x)

• f(x) = -f(-x)

• f(x) = x

Tags

CCSS.HSF.BF.B.3

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

• -2

• 2

• -1

• 1

Tags

CCSS.HSF.IF.A.2

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

• 2

• -1

• 1

• -2

Tags

CCSS.HSF.IF.A.2

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

• -2

• 2

• 1

• 0

Tags

CCSS.HSF.IF.A.2

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)

Tags

CCSS.HSF.BF.B.3

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

• -8

• 8

• 0

• 4

Tags

CCSS.HSF.IF.A.2

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

• 1

• 0

• -5

• 5

Tags

CCSS.HSF.IF.A.2

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)

Tags

CCSS.HSF.BF.B.3

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

• 5

• -1

• 1

• 0

Tags

CCSS.HSF.IF.A.2