Find the constant a such that the function is continuous on the entire real line.

Question

anonymous · Answer

$$f(x) = 2, x \le -1$$$$f(x) = ax+b, -1<x<3$$
$$f(x) = -2, x \ge3$$

anonymous · Answer

$$\text{Let}~~ f_1(x) = 2,~f_2(x) = ax+b,~ \text{and}~f_3(x) = -2$$For these to be continuous f1 = f2 at x=-1 and f2=f3 at x = 3. Therefore, $$f_2(-1) = 2 ~~\text{and} ~~ f_2(3) = -2 $$This can be expressed as $$2 = a(-1) + b ~~\text{and} ~~ -2 = a(3) + b$$Solving simultaneously for a and b, we find that a = -1 and b = 1

anonymous · Answer

Hey, thanks! Don't know why I didn't see that before.