Evaluate the limit of a piecewise function with a hole

The video tutorial explains how to evaluate limits and identify holes in functions. It begins with an introduction to the concept of limits and holes, followed by a step-by-step guide on evaluating limits using algebraic expressions. The tutorial covers factoring techniques to simplify expressions and solve the problem. Finally, it concludes with the final calculations and the solution, demonstrating the process of finding the limit as x approaches a specific value.

What is the purpose of evaluating the left and right-hand limits at a point where there is a hole in the function?

• To determine the continuity of the function

• To calculate the value of the function at that point

• To find the maximum value of the function

• To find the derivative at that point

Which method is used to factor the expression X^2 - 16?

• Difference of two squares

• Synthetic division

• Completing the square

• Quadratic formula

When factoring a trinomial, what should the middle term equal?

• The product of the roots

• The sum of the roots

• The coefficient of the highest degree term

• The constant term

What is the result of simplifying the expression 2X^2 + 7X - 4?

• (2X + 4)(X - 1)

• (2X + 1)(X - 4)

• (2X - 1)(X + 4)

• (2X - 4)(X + 1)

What is the final answer when evaluating the limit as X approaches -4?

• -9/8

• -8/9

• 8/9

• 9/8