If , what is the removable discontinuity (hole) in the graph of ?

Answer and explanation

Correct answer: B.

  1. Step 1: Factor the numerator: .
  2. Step 2: For , simplify: .
  3. Step 3: Since cancels from numerator and denominator, a removable discontinuity occurs at .
  4. Step 4: Evaluate the continuous extension at : .
  5. Step 5: The hole is at the coordinate point .
Answer
.
Why not the others: '' evaluates the unsimplified numerator; '' is an -intercept, not a discontinuity; '' squares the input 4.

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