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)?
What must the value of a?
Hello Guest!
\(f(x) = x + 2\ \color{blue}if\ x > 3\\ f(x) = 2x^2 + 2x + a\ \color{blue}if\ x <= 3 \)
\(3+2=2\cdot3^2+2\cdot 3+a\\ a=3+2-2\cdot 3^2-2\cdot 3\)
\(a=-19\)
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