Question

Find the points at which the following function is discontinuous.Indicate the intervals at which the function is continuous.

f(x)= (x^2 if x<-1), (|x| if -1<x<=1), (3x+1 if 1<x)

Answer 1

looks like x = -1 is NOT included in any of the functions.

Answer 2

f is also discontinuous at x=1, since f(1) = 1, but f(1+h) = 4+h, which does not equal 1, no matter how small h is.

Answer 3

make that f(1+h) = 4 + 3h, but it's still nowhere near 1.