Find the values of a and b so there is no jump discontinuity in the function. f(x) = { 2, x < 0 ax + b, 0 ≤ x ≤ 5 −3x + 7, x > 5

Answer 1

We need the piecewise function to agree on its value at the overlapping points. Therefore, at x = 0, we need:

a(0) + b = 2

b = 2

and at x = 5, we need:

5a + 2 = -8

5a = -10

a = -2