Given $$f ( x ) = \frac { x ^ { 2 } - 16 } { x + 4 } , g ( x ) = x - 4$$

question 61

Multiple Choice

Given $$f ( x ) = \frac { x ^ { 2 } - 16 } { x + 4 } , g ( x ) = x - 4$$ .Complete the table and explain how the two functions differ. $$\begin{array} { | c | c | c | c | c | c | c | c | } \hline x & - 6 & - 5.5 & - 5 & - 4.5 & - 4 & - 3.5 & - 3 \\\hline f ( x ) & & & & & & & \\\hline g ( x ) & & & & & & & \\\hline\end{array}$$
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• A)​\[\begin{array} { | c | c | c | c | c | c | c | c | }
• \hline x & - 6 & - 5.5 & - 5 & - 4.5 & - 4 & - 3.5 & - 3 \\
• \hline f ( x ) & - 10 & - 9.5 & - 9 & - 8.5 & \text { Undefined } & - 7.5 & - 7 \\
• \hline g ( x ) & - 10 & - 9.5 & - 9 & - 8.5 & - 8 & - 7.5 & - 7 \\
• \hline
• \end{array}\] The graph of f(x)= g(x)except when x = -4.Because the factor x + 4 canceled,there is a hole in the graph of f(x)when x = -4.
• B)​ \[\begin{array} { | c | c | c | c | c | c | c | c | }
• \hline x & - 6 & - 5.5 & - 5 & - 4.5 & - 4 & - 3.5 & - 3 \\
• \hline f ( x ) & - 10 & - 9.5 & - 9 & - 8.5 & - 8 & \text { Undefined } & - 7 \\
• \hline g ( x ) & - 10 & - 9.5 & - 9 & - 8.5 & - 8 & - 7.5 & - 7 \\
• \hline
• \end{array}\]
• The graph of f(x)= g(x)except when x = -3.5.Because the factor x + 4 canceled,there is a hole in the graph of f(x)when x = -3.5.
• C)​ \[\begin{array} { | c | c | c | c | c | c | c | c | }
• \hline x & - 6 & - 5.5 & - 5 & - 4.5 & - 4 & - 3.5 & - 3 \\
• \hline f ( x ) & - 10 & - 9.5 & - 9 & \text { Undefined } & - 8 & - 7.5 & - 7 \\
• \hline g ( x ) & - 10 & - 9.5 & - 9 & - 8.5 & - 8 & - 7.5 & - 7 \\
• \hline
• \end{array}\]
• The graph of f(x)= g(x)except when x = -4.5.Because the factor x + 4 canceled,there is a hole in the graph of f(x)when x = -4.5.
• D)​ \[\begin{array} { | c | c | c | c | c | c | c | c | }
• \hline x & - 6 & - 5.5 & - 5 & - 4.5 & - 4 & - 3.5 & - 3 \\
• \hline f ( x ) & - 10 & - 9.5 & \text { Undefined } & - 8.5 & - 8 & - 7.5 & - 7 \\
• \hline g ( x ) & - 10 & - 9.5 & - 9 & - 8.5 & - 8 & - 7.5 & - 7 \\
• \hline
• \end{array}\]
• The graph of f(x)= g(x)except when x = -5.Because the factor x + 4 canceled,there is a hole in the graph of f(x)when x = -5.
• E)​ \[\begin{array} { | c | c | c | c | c | c | c | c | }
• \hline x & - 6 & - 5.5 & - 5 & - 4.5 & - 4 & - 3.5 & - 3 \\
• \hline f ( x ) & - 10 & \text { Undefined } & - 9 & - 8.5 & - 8 & - 7.5 & - 7 \\
• \hline g ( x ) & - 10 & - 9.5 & - 9 & - 8.5 & - 8 & - 7.5 & - 7 \\
• \hline
• \end{array}\]
• The graph of f(x)= g(x)except when x = -5.5.Because the factor x + 4 canceled,there is a hole in the graph of f(x)when x = -5.5.​

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