QuestionFind $\lim _{x \rightarrow 3} f(x)$ for the piecewise function: $f(x) = -9 + 4x$ (for $x<3$) and $f(x) = -6 + x^{2}$ (for $x>3$).

Studdy Solution
Now that we have both the left-hand limit and the right-hand limit, we can determine the limit of $f(x)$ as $x$ approaches3. If the left-hand limit and the right-hand limit are equal, then the limit of the function at that point is that common value.
$$\lim{{x \rightarrow3}} f(x) =3$$The limit of the function $f(x)$ as $x$ approaches3 is3.