Question

what value of f is not continuous? which of these discontinuities are removable?

f(x)={-2x+3 , x<1
x^2 , x≥1

Answer 1

f appears to be continuous across the full set of all real numbers for this scenario is (both functions appear to be continuous across the set of R). The point x --> 1 on left and right need to be tested to make sure they approach the same value, since this is a piecewise function.

So if you plug in x=1 into both equations do you get the same value?

Does the value 'jump'?

Could you use any type of algebra to remove the jump if it exists anyway (keep in mind the two functions are completely separate from each other.