+0  
 
+7
368
2
avatar+737 

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
avatar+93038 
+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   

 

 

 

cool cool cool               

CPhill  Aug 28, 2017
edited by CPhill  Aug 28, 2017
 #2
avatar+737 
+5

Thank you!

MIRB16  Aug 28, 2017

7 Online Users

avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.