Explain what it means to say that lim f(x) = 6 and lim f(x) = 9. X - 1T x - 1 As x approaches 1 from the right, f(x) approaches 6. As x approaches 1 from the left, f(x) approaches 9. O As x approaches 1, f(x) approaches 6, but f(1) = 9. As x approaches 1 from the left, f(x) approaches 6. As x approaches 1 from the right, f(x) approaches 9. O As x approaches 1, f(x) approaches 9, but f(1) = 6. In this situation is it possible that lim f(x) exists? Explain. x - 1 Yes, f(x) could have a hole at (1, 6) and be defined such that f( 1) = 9. Yes, f(x) could have a hole at (1, 9) and be defined such that f( 1) - 6. Yes, if f(x) has a vertical asymptote at x = 1, it can be defined such that lim f(x) - 6, lim f(x) = 9, and lim f(x) exists. x 1 X -it X - 1 No, lim f(x) cannot exist if lim f(x) # lim f(x). x - 1 x- 1 x-1

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