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Let

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

f(x) = ax^2 + 7x - 4 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 10, 2021
 #1
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Let

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

f(x) = ax^2 + 7x - 4 if x > 3

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

 

Hello Guest!

 

\(f_1(x) = 3x^2 - 2\\ f_1(3) = 3\cdot 9 - 2=25\)

\(f_2(x) = ax^2 + 7x - 4=25\\ f_2(3) = a\cdot 9 + 7\cdot 3 - 4=25\\ 9a=25-21+4=8\)

\(a=\dfrac{8}{9}\)

 a, if the graph of y = f(x) is continuous, is \(\dfrac{8}{9}.\)

 

The graph of y = f(x) is \(f_1(x) = 3x^2 - 2\ |\ if\ x\ \leq 3\\ f_2(x) = \dfrac{8}{9}x^2 + 7x - 4\ |\ if\ x > 3\)

laugh  !
 

 Aug 10, 2021
edited by asinus  Aug 10, 2021
edited by asinus  Aug 10, 2021

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