Consider the following fx 5x x 2 Find the xvalue at which f

Consider the following f(x) = -5x, x 2 Find the x-value at which f is not continuous. Is the discontinuity removable? (Enter NONE in any unused answers blanks)

Solution

A function that is continuousis a function whose graph has no breaks in it; i.e. it is a continuous curve

f(2) = -5*2 as x<= 2

= -10

And f(2) = (-2)^2 -2(-2) +3 = 4 +4 +3 = 11 for x>2

AS LHS is not equal to RHS

So, at x =2 graph is discontinous

This is Jump discontinuities and can be removed.