Posted by **Derrick** on Friday, September 16, 2011 at 3:17pm.

For what values of a and b that make the function f continuous everywhere.

f(x)={(x^2-4)/(x-2) if x<2

ax^2-bx-18 if 2<x<3

10x-a+b if x>3

- calculus -
**MathMate**, Friday, September 16, 2011 at 4:31pm
There are three segments of functions, and two possibly discontinuous points, at x=2 and x=3.

Equate the adjacent segments to find the value of a and b that make the segments have the same values at x=2 and x=3.

Finally, check that the limits approaching from each side (2- and 2+, 3- and 3+) of the combined function are identical. They should be if the function is continuous.

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