Evaluate the limit of a rational expression by applying direct substitution

The video tutorial explains why direct substitution cannot be used when evaluating the limit of a function as x approaches 2 due to a zero in the denominator, making the function undefined. The instructor demonstrates how to simplify the expression by factoring the numerator and denominator, allowing the limit to be evaluated as x approaches 2. The result is a hole in the graph, and the limit is calculated to be 5. The lesson concludes with a reminder about the test's free response portion and an optional graph confirmation.

Why can't we use direct substitution when the denominator becomes zero?

• Because it results in a zero in the numerator

• Because it makes the function undefined

• Because it simplifies the function

• Because it changes the limit

What mathematical technique is suggested to simplify the problem when direct substitution fails?

• Completing the square

• Factoring

• Integration

• Differentiation

What is the simplified expression for the limit as X approaches 2?

• X - 2

• X - 3

• X + 2

• X + 3

What is the term used to describe the point where the function is not defined but the limit exists?

• Asymptote

• Discontinuity

• Hole

• Intercept

What is the value at the hole for the function as X approaches 2?

• 5

• 6

• 4

• 3