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# Help ASAP

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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).

Jul 22, 2020

#1
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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

Jul 22, 2020
#2
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How do we find the equation of a continuous piecewise function though?

Thank you very much!

Jul 22, 2020
#3
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Well, given a and b we can write

Alan  Jul 22, 2020
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Thank you!

Jul 22, 2020