calculus

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Find the constants a & b such that the function f(x)={2 if ≤ -1
{ax+b if -1<x<3
{-2 if x ≥3
is continuous on the entire real line

  • calculus -

    the left-side transition point is (-1,2)
    so (-1,2) should satisfy y = ax+b
    2 = -a + b

    the right-side transition point is (3, -2)
    so (3,-2) should also satisfy y = ax + b
    -2 = 3a + b
    subtract those two equations
    4a = -4
    a = -1
    then b = 2+a = 2-1 = 1

    a=-1 , b=1

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