The video tutorial explains how to evaluate limits for piecewise functions, focusing on a specific example where a function has a hole at X = 1. The instructor demonstrates how to visualize the graph of the function, which is a parabola with a shift, and explains the concept of a hole in the graph. The tutorial emphasizes understanding the limit as X approaches the hole and determining the function's value at that point. The lesson concludes with a summary of the graphical approach to evaluating limits.

What is the value of the function X^2 + 3 at X = 1?

• 4

• 3

• 2

• 1

How does the graph of X^2 + 3 look like?

• A straight line

• A hyperbola

• A circle

• A parabola shifted up by three units

What happens at X = 1 on the graph of the function?

• There is a vertical asymptote

• There is a hole

• There is a peak

• There is a trough

What is the limit of the function as X approaches 1?

• 3

• 2

• 1

• 4

Why is algebraic manipulation not necessary to find the limit in this case?

• Because the function is continuous

• Because the function is undefined

• Because the graph clearly shows the limit

• Because the function is linear