Question

Determine all numbers at which the function is continuous.

Answer 1

(-infinity,-1)U(-1,infinity)

Explanation:

plug in the number where the piecewise function changes which is -1 and 1

(-1)^2-(-1)-2 =0

(-1)=-1

These aren't equal so the function is discontinuous at x = -1 because of a jump

(1) = 1

-2(1) + 3 = 1

These are equal so the function is continuous at x = 1

So from negative infinity to -1 the function is continuous and from -1 to infinity

(-infinity,-1)U(-1,infinity)