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Let \[f(x) = \begin{cases} 3x^2 + 2&\text{if } x\le 3, \\ ax - 1 &\text{if } x>3. \end{cases} \]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).

 Apr 27, 2022
 #1
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Let x =  3      and set the two functions eaual

 

3(3)^2  +  2  =   a(3)  -  1

 

27 + 2  = 3a   -  1

 

29  =  3a    - 1

 

29   +  1  = 3a

 

30 =  3a

 

a  = 30   / 3   =    10

 

 

cool cool cool

 Apr 27, 2022

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