Let f(x) = cx + 3x 3. if x < 4 if x 4. For what value of the constant c is the function f continuous on (-, )? Step 1 Recall that a function f is continuous at a number a if the following holds. lim f(x) = f(a) x-a We are given the following. cx + 3x if x < 4 f(x) We note that for all values of the constant c the function f is continuous on both (-, 4) and (4, w). The only case that we need to consider is when x = 4. For the function f to be continuous on (-, ), we need to ensure that there is not a discontinuity To do so, we must determine the value of c such that the following holds. lim f(x) = lim f(x) X-4M Find the following limits. lim f(x) = x-4 lim (cx + 3x) X-M lim f(x) = lim +(x-cx)