Part A: Explain the meaning of the following equation. Iim f(x) = 3
x → 9

A.)f(x) = 3 for all values of x.

B.)The values of f(x) can be made as close to 9 as we like by taking x sufficiently close to 3.

C.) The values of f(x) can be made as close to 3 as we like by taking x sufficiently close to 9.

D.) If |x1 − 9| < |x2 − 9|, then |f(x1) − 3|≤ |f(x2) − 3|.

E.) If |x1 − 9| < |x2 − 9|, then |f(x1) − 3| < |f(x2) − 3|.

Part B is it possible for this statement to be true and yet
f(9) = 7?
Explain.

A.) Yes, the graph could have a hole at (9, 3) and be defined such that f(9) = 7.

B.) Yes, the graph could have a vertical asymptote at x = 9 and be defined such that f(9) = 7.

C.) No, if f(9) = 7, then
lim
x→9
f(x) = 7.

D.) No, if
lim
x→9
f(x) = 3, then f(9) = 3.