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).

MIRB16
Aug 28, 2017

#1**+2 **

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

CPhill
Aug 28, 2017