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).
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
