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# piecewise defined function

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Let

f(x) = 2x^2 - 4 if x <= 2,

ax + 5 if x > 2.

Find a if the graph of y = f(x) is continuous (which means the graph can be drawn without lifting your pencil from the paper).

Oct 14, 2020

#1
+10820
+1

Let

f(x) = 2x^2 - 4 if x <= 2    and    ax+5  if  x > 2

Find a if the graph of y = f(x) is continuous. (which means the graph can be drawn without lifting your pencil from the paper).

Hello Guest!

$$\color{BrickRed}f(x)=2x^2-4=ax+5\\ x=2\\ 2\cdot 2^2-4=2a+5\\ a=(2\cdot 2^2-4-5)/2$$

$$\large a=-\frac{1}{2}$$

!

Oct 14, 2020