Question

x(squared)+8x+17 if x < or = -4

Let f(x)= 2 if x= -4
-x(squared)-8x-15 if x > -4

Show that f(x) has a removable discontinuity at x=–4 and determine what value for f(–4) would make f(x) continuous at x=–4.
Must redefine f(–4)=____

Answer 1

Compute the limit x --> -4 of f(x)

You should find that this limit exists and is equal to 1 (you have to show that the left and right limits exist and are the same). By definition a function is continuous if

f(y) = lim x --->y of f(x)

for all y.