Given

f ( x ) = \frac { x ^ { 2 } - 36 } { x + 6 } , g ( x ) = x - 6

.Complete the table and explain how the two functions differ.

\begin{array} { | c | c | c | c | c | c | c | c | } \hline x & - 8 & - 7.5 & - 7 & - 6.5 & - 6 & - 5.5 & - 5 \\\hline f ( x ) & & & & & & & \\\hline g ( x ) & & & & & & & \\\hline\end{array}

\begin{array} { | c | c | c | c | c | c | c | c | } \hline x & - 8 & - 7.5 & - 7 & - 6.5 & - 6 & - 5.5 & - 5 \\\hline f ( x ) & - 14 & - 13.5 & \text { Undefined } & - 12.5 & - 12 & - 11.5 & - 11 \\\hline g ( x ) & - 14 & - 13.5 & - 13 & - 12.5 & - 12 & - 11.5 & - 11 \\\hline\end{array}

The graph of f(x)= g(x)except when x = -7.Because the factor x + 6 canceled,there is a hole in the graph of f(x)when x = -7.
B)

\begin{array} { | c | c | c | c | c | c | c | c | } \hline x & - 8 & - 7.5 & - 7 & - 6.5 & - 6 & - 5.5 & - 5 \\\hline f ( x ) & - 14 & \text { Undefined } & - 13 & - 12.5 & - 12 & - 11.5 & - 11 \\\hline g ( x ) & - 14 & - 13.5 & - 13 & - 12.5 & - 12 & - 11.5 & - 11 \\\hline\end{array}

The graph of f(x)= g(x)except when x = -7.5.Because the factor x + 6 canceled,there is a hole in the graph of f(x)when x = -7.5.
C)

\begin{array} { | c | c | c | c | c | c | c | c | } \hline x & - 8 & - 7.5 & - 7 & - 6.5 & - 6 & - 5.5 & - 5 \\\hline f ( x ) & - 14 & - 13.5 & - 13 & \text { Undefined } & - 12 & - 11.5 & - 11 \\\hline g ( x ) & - 14 & - 13.5 & - 13 & - 12.5 & - 12 & - 11.5 & - 11 \\\hline\end{array}

The graph of f(x)= g(x)except when x = -6.5.Because the factor x + 6 canceled,there is a hole in the graph of f(x)when x = -6.5.
D)

\begin{array} { | c | c | c | c | c | c | c | c | } \hline x & - 8 & - 7.5 & - 7 & - 6.5 & - 6 & - 5.5 & - 5 \\\hline f ( x ) & - 14 & - 13.5 & - 13 & - 12.5 & \text { Undefined } & - 11.5 & - 11 \\\hline g ( x ) & - 14 & - 13.5 & - 13 & - 12.5 & - 12 & - 11.5 & - 11 \\\hline\end{array}

The graph of f(x)= g(x)except when x = -6.Because the factor x + 6 canceled,there is a hole in the graph of f(x)when x = -6.
E)

\begin{array} { | c | c | c | c | c | c | c | c | } \hline x & - 8 & - 7.5 & - 7 & - 6.5 & - 6 & - 5.5 & - 5 \\\hline f ( x ) & - 14 & - 13.5 & - 13 & - 12.5 & - 12 & \text { Undefined } & - 11 \\\hline g ( x ) & - 14 & - 13.5 & - 13 & - 12.5 & - 12 & - 11.5 & - 11 \\\hline\end{array}

The graph of f(x)= g(x)except when x = -5.5.Because the factor x + 6 canceled,there is a hole in the graph f(x)when x = -5.5.

Determine the Equations of the Vertical and Horizontal Asymptotes of the Graph

Multiple Choice