Understanding Limits of Piece-Wise Functions

The video tutorial explores the concept of limits using a piece-wise defined function. It examines the limits as X approaches 1 and 3, demonstrating how to determine if a limit exists by evaluating the function from both sides. The tutorial uses both analytical and graphical methods to explain why the limit at X=1 does not exist and how the limit at X=3 can be determined through direct substitution.

What is the equation of the graph when x is less than 1?

• Y = 3X - 2

• Y = X + 1

• Y = -X - 1

• Y = 2X - 1

What is the equation of the graph when x is greater than or equal to 1?

• Y = 3X - 2

• Y = X + 1

• Y = -X - 1

• Y = 2X - 1

What is the function value as x approaches 1 from the left?

• 2

• 0

• -2

• 1

What is the function value as x approaches 1 from the right?

• 1

• -2

• 0

• 2

Why does the limit not exist at x = 1?

• The function is undefined at x = 1

• The function has a vertical asymptote at x = 1

• The function values from the left and right are different

• The function is continuous at x = 1

What is the function value as x approaches 3?

• -1

• -4

• -3

• -2

How can the limit as x approaches 3 be determined?

• By using L'Hôpital's rule

• By direct substitution

• By evaluating both sides separately

• By finding the derivative

What is the graphical representation of the limit as x approaches 1?

• The function values converge to a single point

• The function values diverge

• The function values approach different points from each side

• The function is continuous

What is the graphical representation of the limit as x approaches 3?

• The function values converge to a single point

• The function values diverge

• The function values approach different points from each side

• The function is discontinuous

What is the function value of F(3)?

• -2

• -3

• -4

• -1