+753 Let \(f(x) = \left\{ \begin{array}{cl} ax+3, &\text{ if }x>2, \\ x-5 &\text{ if } -2 \le x \le 2, \\ 2x-b &\text{ if } x <-2. \end{array} \right.\)Find a+b if the piecewise function is continuous (which means that its graph can be drawn without lifting your pencil from the paper).
+129852
We need to find values for "a" and "b" that will make the graph continuous
First, let x = -2
And solve this for :b"
-2 - 5 =2 (-2) - b
-7 = -4 - b
-3 = -b
b = 3
Next, let x = 2
And solve this for "a"
2 - 5 + a(2) + 3
-3 = 2a + 3
-6 = 2a
a = -3
So we have that
-3x + 3, if x > 2
f(x) = x - 5, if -2 ≤ x ≤ 2
2x - 3, if x < -2
Here's the graph from left to right : https://www.desmos.com/calculator/ibd5jn8m8s
