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Shown below are six statements about functions. Match each statement to one of the functions shown below which BEST matches that statement.

1. $\lim_{x\to 3^+} f(x)$ and $\lim_{x\to 3^-} f(x)$ both exist and are finite, but they are not equal.
2. The graph of $y=f(x)$ has vertical tangent line at $(3,f(3))$
3. $\lim_{x\to 3^-}f(x)=-\infty$.
4. $\lim_{x\to 3^+}f(x)$ exists but $\lim_{x\to 3^-}f(x)$ does not.
5. $\lim_{x\to 3}f(x)=\infty$.
6. $\lim_{x\to 3}f(x)$ exists but $f$ is not continuous at 3.

A. $f(x)=\sqrt{x- 3}$
B. $f(x)=\frac{1}{(x- 3)^2}$
C. $f(x)=\left\lbrace\begin{array}{ll}4 x &\mbox{if }x<3\\ 0 &\mbox{if }x=3\\ 24 - 4 x &\mbox{if }x>3\\ \end{array}\right.$
D. $f(x)=\frac{1}{x- 3}$
E. $f(x)=\left\lbrace\begin{array}{ll}4 x &\mbox{if }x<3\\ 0 &\mbox{if }x=3\\ 4 x - 24 &\mbox{if }x>3 \\ \end{array}\right.$
F. $f(x)=\left\lbrace\begin{array}{ll}\cos\left(\frac{1}{x- 3}\right) &\mbox{if }x<3\\ 0 &\mbox{if }x=3\\ 4 x + 24 &\mbox{if }x>3\\ \end{array}\right.$

Your overall score for this problem is 