For real numbers $x$, let \[f(x) = \left\{ \begin{array}{cl} x+2 &\text{ if }x>3, \\ 2x+a &\text{ if }x\le 3. \end{array} \right.\]What must the value of $a$ be to make the piecewise function continuous (which means that its graph can be drawn without lifting your pencil from the paper)?

Guest Aug 23, 2018

#1**+2 **

\(f(x) = \left\{ \begin{array}{cl} x+2 &\text{ if }x>3, \\ 2x+a &\text{ if }x\le 3. \end{array} \right. \)

Let x = 3 and set the functions equal.... we have

3 + 2 = 2(3) + a

5 = 6 + a

5 - 6 = a

- 1 = a

See the graph here that shows that this value of a makes the function continuous :

https://www.desmos.com/calculator/ux7xrnhaxi

CPhill Aug 23, 2018