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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).

 Mar 5, 2021
 #1
avatar+207 
+1

Hey there.

 

Might need some confirmation on this, but because it is continuous, i think that means that at x=3, the top and bottom are equal to eachother.

so: 3x^2 + 2 = ax - 1

 

Using this just rearrange and you can find a with x = 3

 

3*9+2=3*a-1

29=3a-1

30=3a

10=a

 

Hope this helps, im pretty sure thats how it works :)

 Mar 5, 2021
edited by lhyla02  Mar 5, 2021
edited by lhyla02  Mar 5, 2021

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