Let
\[f(x)={ax+3, if x>2,x−5 if −2≤x≤2,2x−b if x<−2.\]
Find a+b if the piecewise function is continuous. (which means that its graph can be drawn without lifting your pencil from the paper).
If the curve is continuous then we must have:
At x = 2: a*2 + 3 = 2 - 5 or 2a = -6 so a = -3
At x = -2: 2*(-2) - b = -2 - 5 or -4 - b = -7 so b = 3
How do we find the equation of a continuous piecewise function though?
Thank you very much!
Well, given a and b we can write
Thank you!
+479 
