Continuity check
Let be a real number. Consider the function . Is this function continuous for all values of ?
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
Moderator note:
Simple standard approach.
For negative x, |x| = -x, so the function is equal to 0.
At x = 0, the value is also 0.
And for positive x, the value is 2x.
None of these is discontinuous and at x=0 there is not a discontinuity of any kind either.