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. $$\begin{array} { | c | c | c | c | c | c | c | c | } \hline x & - 6 & - 5.5 & - 5 & - 4.5 & - 4 & - 3.5 & - 3 \\\hline f ( x ) & & & & & & & \\\hline g ( x ) & & & & & & & \\\hline\end{array}$$
​

• 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.​

---

Definitions:

Government

The system by which a state or community is controlled or regulated, typically consisting of legislature, executive, and judiciary branches.

Regulators

Authorities or agencies responsible for overseeing and enforcing compliance with laws, rules, or regulations in various fields.

Sustainability

The ability to maintain or improve certain processes or states indefinitely, often referring to environmental, economic, and social well-being.

Environmental Activists

Individuals or groups who actively promote the protection of the environment and advocate for policies or practices that minimize harm to natural ecosystems.