Posted by Maria on Tuesday, December 6, 2011 at 10:55pm.
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  Reiny, Tuesday, December 6, 2011 at 11:50pm
the leftside transition point is (1,2)
so (1,2) should satisfy y = ax+b
2 = a + b
the rightside 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 = 21 = 1
a=1 , b=1