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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).

HelpBot Jul 22, 2020

Alan · Answer 1 · 2020-07-22T09:03:33

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

HelpBot · Answer 2 · 2020-07-22T09:05:40

How do we find the equation of a continuous piecewise function though?

Thank you very much!

HelpBot · Answer 3 · 2020-07-22T11:06:14

Thank you!