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).

wizzymath Mar 5, 2021

#1**+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 :)

lhyla02 Mar 5, 2021