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calculus

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find the constants a and b so that the function is continuous on the entire real line. F(x)= 3, x≤-1
ax+b, -1<x<2
-3,x≥2 Help???

  • calculus -

    A little more legibly,

    f(x)
    = 3 for x<=1
    = ax+b for 1<x<2
    = -3 for x>=2

    So, you need to find a line connecting (-1,3) with (2,-3) so there are no holes in the graph.

    That's just a simple two-point line problem:

    (y-3)/(x+1) = -6/3 = -2
    y-3 = -2(x+1)
    y = -2x + 1

    So, f(x) = -2x+1 for -1<x<2

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