<p>Can someone please explain to me how you approach this question, I'm horrible at Calc...and I'm sure this is easy enough for you guys.</p>
<p>find the constants a and b such that the function is continuous on the entire real line</p>
<p>f(x) = 2 ||x <= -1
ax +b || -1 < x < 3
-2 || x >= 3</p>
<p>Thanks!</p>
<p>Basically, the function is defined for x<=-1 and >=3. That means you're trying to fill the gap between x=-1 and x=3. Those points are (-1,2) and (3,-2). You are to fill this gap with a line connecting those points, so ax+b= -x+1. a=-1, b=1.</p>
<p>Another way of solving this (not necessarily easier!) is to use</p>
<p>ax + b = f(-1) when x = -1 i.e. -a + b = 2
and ax + b = f(3) when x=3 i.e. 3a + b = -2</p>
<p>Solve for a and b: (3 + 1)a = -2 -2, or 4a = -4, or a=-1
and b = 2+ a = 1</p>
<p>Optimizerdad, our two solutions seem to have the same math behind it, just represented in different forms. I think the preferred solution would be the one you are most comfortable dealing with--visualizing what is happening or analyzing the information you have to find a solution.</p>
<p>No argument here...</p>
<p>Yeah...I'm just saying...lol I'm just trying to procrastinate from my work...</p>