Testing Polynomial Symmetry: Even vs Odd Functions

What is the main topic discussed in the video?

• Symmetry in functions

• Derivatives of functions

• Limits and continuity

• Integration techniques

Which of the following is true for an even function?

• It is symmetric about the X-axis

• It is symmetric about the origin

• It is symmetric about the Y-axis

• It has no symmetry

What is the condition for a function to be even?

• f(x) = -f(x)

• f(x) = f(-x)

• f(x) = x^2

• f(x) = x^3

In the example provided, what is the function f(x) = 3x^4 + 5 classified as?

• Linear function

• Neither even nor odd

• Even function

• Odd function

What happens when you replace x with -x in the function f(x) = 3x^4 + 5?

• The function becomes zero

• The function remains the same

• The function becomes undefined

• The function becomes negative

Which of the following is true for an odd function?

• It has no symmetry

• It is symmetric about the X-axis

• It is symmetric about the origin

• It is symmetric about the Y-axis

What is the condition for a function to be odd?

• f(x) = -f(x)

• f(x) = f(-x)

• f(x) = x^2

• f(x) = -f(-x)

In the example provided, what is the function f(x) = x^3 - x classified as?

• Odd function

• Neither even nor odd

• Even function

• Linear function

What happens when you replace x with -x in the function f(x) = x^3 - x?

• The function remains the same

• The function becomes negative

• The function becomes zero

• The function becomes undefined

What is a quick way to identify an odd function?

• The function becomes undefined

• The function becomes zero

• All signs of the terms flip

• All signs of the terms remain the same