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# help function

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For real numbers x, let

f(x) = x + 2 if x > 3

f(x) = 2x^2 + 2x + a if x <= 3

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)?

Oct 24, 2021

#1
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What must the value of a?

Hello Guest!

$$f(x) = x + 2\ \color{blue}if\ x > 3\\ f(x) = 2x^2 + 2x + a\ \color{blue}if\ x <= 3$$

$$3+2=2\cdot3^2+2\cdot 3+a\\ a=3+2-2\cdot 3^2-2\cdot 3$$

$$a=-19$$

!

Oct 24, 2021