Posted by fernando on .
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 
Steve,
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 twopoint line problem:
(y3)/(x+1) = 6/3 = 2
y3 = 2(x+1)
y = 2x + 1
So, f(x) = 2x+1 for 1<x<2