Step 1 Recall that a function f is continuous at a number a if the following holds. lim_ f(x) = f(a) We are given the following. cx² + 9x f(x) = x³ - cx if x < 4 if x 24 We note that for all values of the constant c the function f is continuous on both (-[infinity]o, 4) and (4, [infinity]). The only case that we need to consider is when x = 4. For the function f to be continuous on (-[infinity]o, o), we need to ensure that there is not a discontinuity at x = 4. To do so, we must determine the value of c such that the following holds. lim f(x) = lim f(x) X-4- x+4+ Find the following limits. lim f(x) = lim (cx² + 9x) x+4 lim (x³ - cx) lim f(x).