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Given f(x)=x2−16x+4,g(x)=x−4f ( x ) = \frac { x ^ { 2 } - 16 } { x + 4 } , g ( x ) = x - 4

Question 61

Multiple Choice

Given f(x) =x2−16x+4,g(x) =x−4f ( x ) = \frac { x ^ { 2 } - 16 } { x + 4 } , g ( x ) = x - 4 .Complete the table and explain how the two functions differ. x−6−5.5−5−4.5−4−3.5−3f(x) g(x) \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) ​ x−6−5.5−5−4.5−4−3.5−3f(x) −10−9.5−9−8.5 Undefined −7.5−7g(x) −10−9.5−9−8.5−8−7.5−7\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) ​ x−6−5.5−5−4.5−4−3.5−3f(x) −10−9.5−9−8.5−8 Undefined −7g(x) −10−9.5−9−8.5−8−7.5−7\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) ​ x−6−5.5−5−4.5−4−3.5−3f(x) −10−9.5−9 Undefined −8−7.5−7g(x) −10−9.5−9−8.5−8−7.5−7\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) ​ x−6−5.5−5−4.5−4−3.5−3f(x) −10−9.5 Undefined −8.5−8−7.5−7g(x) −10−9.5−9−8.5−8−7.5−7\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) ​ x−6−5.5−5−4.5−4−3.5−3f(x) −10 Undefined −9−8.5−8−7.5−7g(x) −10−9.5−9−8.5−8−7.5−7\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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