aside from the obvious asymptotes,
just check where the definition changes.
does f(2) equal the left and right limits?
Just use x=2 and 4 and evaluate the different pieces.
For example, from the left, f(2) = (2-1)^2/(2+1) = 4/3
watch for holes (when f(x) = 0/0)
on the right, f(2) = (4-4-8)/(4-2) = -4
so, there's a break at x=2
Suppose f(x) =
(x-1)^2/x+1 if x < 2
(x^2-2x-8)/x-4 if 2 <= x < 4
(1/(x-3))+5 if 4 <= x
Identify any points of discontinuity, and determine (giving reasons) if they are removable, infinite (essential), or jump discontinuities. How do I find the continuities in a piece wise function?
1 answer
1 answer