Question

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???

Answer 1

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