n each part below, give an example of a function which satisfies the given criteria. Justify that your xample is correct. You should give the simplest example of which you can think. (i) A function f whose domain is (–1,1) such that lim f(x) = 3 and lim f(x) = -2. T→0+ x→0- ii) lim f(x) = 0. A function f whose domain is (-1,1) such that f(x) > 0 for all x e (-1, 1), and ii) A function f whose domain is R, such that f is not continuous at 0, but fof is continuous at 0.

Consider the following function and graph. (a) lim fcx) つる 1 f(x) x + 2 3 (b) lim flx): Determine whether f(x) approaches o or -o as x approaches -2 from the left and from the right.

Suppose that the graph of a function f is known.  Explain how the graph of of y = f(x) – 2 differs from the graph of y = f(x – 2).

Explain why the function is discontinuous at the given number a. (Select all that apply.) 2x2 – 7x – 4 - if x + 4 f(x) х — 4 a = 4 if x = 4 lim f(x) and lim f(x) are finite, but are not equal. X→4+ X→4- f(4) and lim f(x) are finite, but are not equal. X→4 f(4) is undefined. lim f(x) does not exist. X→4 none of the above