The video tutorial explains how to evaluate limits and continuity in piecewise functions. It begins with an introduction to piecewise functions and the importance of evaluating limits. The tutorial then discusses defining points where functions change and explores graph connectivity options. It emphasizes the need to evaluate continuity at break points by checking limits from both sides. The tutorial concludes by demonstrating how to determine if a function is continuous by comparing limits from the left and right.

What is the result of evaluating the limit as X approaches -1 for the given piecewise function?

• 2

• -1

• 0

• 1

What is a key factor in determining if a piecewise function is continuous at a breakpoint?

• The function's domain

• The function's derivative

• The function's integral

• The equality of limits from both sides

When evaluating a piecewise function at a breakpoint, what should be compared?

• The integral of the function at the breakpoint

• The slope of the function at the breakpoint

• The limits from the left and right of the breakpoint

• The values of the function at the breakpoint

In the example provided, what is the value of the limit from the left and right at zero?

• -1

• 2

• 1

• 0

What does the equality of limits from both sides at zero indicate about the piecewise function?

• The function is continuous

• The function is discontinuous

• The function is undefined

• The function has a jump discontinuity