AP CollegeBoard Test Booklet 6. Continuity A student attempted to confirm that the function f defined by f(x) = 72_721 is continuous at x = 2. In which step, if any, does an error first appear? Step 1: f(x) = $ 4x-6 (I-2)(1+3) 12 -71+10 Step 2: lim f(x) = lim +3 3 (2-2 2) (2-5) 2- 5 Step 3: f(2) = 2+32428-5 = 2- 5 Step 4: lim f(x) = f(2), so f is continuous at x = 2. I-+2 (A) Step 2 B) Step 3 (C) Step 4 (D There is no error in the confirmation. 8. x2 + 2x for x 3 Let f be the piecewise function defined above. Which of the following statements is false? (A) f is continuous at x = 1. (B) f is continuous at I = 2. (C) f is continuous at x = 3. (D) f is continuous at ac = 4. 9. Let fbe the function defined by f(x) = Sx2 + 2 for a 3. If fis continuous at x = 3, what is the value of k ? (A) -7 2 3 (D) 7 (E) There is no such value of k. 10. If the function f is continuous for all real numbers and if f (x) = 2 4w 1+2 when a * -2, then f(-2) = (A) 14 (B) - 2 (C) -1 (D) 0