+0

# help with piecewise defined functions pls

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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).

Mar 5, 2021

#1
+34464
+2

The line of the graph needs to be continuous so

at x = 2        ax+3 has to equal   x-5

ax+3 = x-5

ax = x - 8      at x= 2

a(2) = 2-8

a = -3

and   at  -2          x-5   has to equal 2x-b

x-5 = 2x-b

b+5 = x                for x = -2

b+5 = -2

b = -7

Mar 5, 2021
#3
+34464
+1

*** corrected  ***

Had an incorrect '+' sign:

and   at  -2          x-5   has to equal 2x-b

x-5 = 2x-b

b - 5 = x                for x = -2

b - 5 = -2

b = 3

ElectricPavlov  Mar 5, 2021
#2
+229
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thats wrong but thanks

Mar 5, 2021