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# Function

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48
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Let

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

f(x) = ax^2 - x + 11 if x > 3

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).

Aug 8, 2021

#1
+12222
+1

Let

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

f(x) = ax^2 - x + 11 if x > 3

Find a if the graph of y = f(x) is continuous

Hello Guest!

$$f(3) = 3x^2 + 2=29\\ f(3) = a\cdot 3^2 - 3 + 11=29\\ 9a+8=29\ |\ -8\\ 9a=21\ |\ :9$$

$$a=\dfrac{7}{3}$$

The graph is $$f(x)=3x^2+2\ |\ x\leq3\\ f(x)=\dfrac{7}{3}x^2-x+11\ |\ x>3$$

!

Aug 8, 2021