Suppose f(x)=((x^2)+7x+12)/((x^2)-9)
A. Identify all intervals where fx is continuous
B. For each discontinuity, State which conditions of the continuity test are not met
C. Classify each discontinuity as removable or non removable
Answer:
A: (-infinity, -3), (-3, 3), (3,infinity)
B: For x = -3 and x = 3: The function is not defined at x=a
C: Discontinuities @ x = -3 and x = 3. At x = 3, the limit DNE (NON-REMOVABLE) because the limit as x approaches 3 from the left is -infinity and the limit as x approaches 3 from the right is positive infinity. For -3, it is a removable discontinuity. Since the limit as x approaches -3 from both sides is -.1667, create a peacewise function that specifies if x = -3, then y = -.1667
