choosing the graph of the quotient of two functions\nwhich graph shows $h(x)=\frac{f(x)}{g(x)}$?

Explanation:

Step1: Analyze function values

Find points on (f(x)) and (g(x)) and calculate (\frac{f(x)}{g(x)}). For example, at (x = 0), find (f(0)) and (g(0)) and compute (h(0)=\frac{f(0)}{g(0)}).

Step2: Check asymptotes

Determine where (g(x)=0) as these are vertical - asymptote candidates for (h(x)=\frac{f(x)}{g(x)}). Analyze the behavior of (f(x)) and (g(x)) near these points.

Step3: Analyze end - behavior

Examine the behavior of (f(x)) and (g(x)) as (x\to\pm\infty) to determine the end - behavior of (h(x)).

Answer:

Without specific functions (f(x)) and (g(x)) values, we cannot determine the exact graph. More information about the functions (such as their equations or more detailed point - by - point values) is needed to choose the correct graph of (h(x)=\frac{f(x)}{g(x)}).