In Silicon Valley, a number of computer firms were found to be contaminating underground water supplies with toxic chemicals stored in leaking underground containers. A water quality control agency ordered the companies to take immediate corrective action and contribute to a monetary pool for the testing and cleanup of the underground contamination. Suppose that the required monetary pool (in millions of dollars) is given by the following function, where $$ x $$ is the percentage (expressed as a decimal fraction) of the total contaminant removed. Complete parts (A) through (E). $$ P(x)=\frac{11 x}{1-x} \quad 0 \leq x

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In Silicon Valley, a number of computer firms were found to be contaminating underground water supplies with toxic chemicals stored in leaking underground containers. A water quality control agency ordered the companies to take immediate corrective action and contribute to a monetary pool for the testing and cleanup of the underground contamination. Suppose that the required monetary pool (in millions of dollars) is given by the following function, where $$ x $$ is the percentage (expressed as a decimal fraction) of the total contaminant removed. Complete parts (A) through (E). $$ P(x)=\frac{11 x}{1-x} \quad 0 \leq x<1 $$ Find the horizontal asymptote(s), if any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The horizontal asymptote(s) is (are) $$ y= $$ (Simplify your answer. Use a comma to separate answers as needed) B. There are no horizontal asymptotes. (D) Find the $$ x $$ - and $$ y $$-intercepts. Find the $$ x $$-intercept(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The $$ x $$-intercept(s) is (are) $$ x= $$ (Simplify your answer. Use a comma to separate answers as needed.) B. There are no $$ x $$-intercepts. B.

UpStudy AI · Accepted Answer

**A. Horizontal Asymptote**

The function is 
$$
P(x)=\frac{11x}{1-x}, \quad 0\le x<1.
$$
A horizontal asymptote is determined by taking the limit as $$ x $$ approaches infinity (or negative infinity). However, since the domain is restricted to $$ 0\le x<1 $$, the function never attains arbitrarily large values of $$ x $$. Even though for a rational function with numerator and denominator of the same degree one might normally find a horizontal asymptote by taking the ratio of the leading coefficients, this is not applicable here because the domain does not include values near $$ \infty $$ or $$-\infty$$.

Thus, there are no horizontal asymptotes.

**B. Intercepts**

1. **$$ x $$-intercept:**  
   To find the $$ x $$-intercept, set 
   $$
   P(x)=\frac{11x}{1-x}=0.
   $$
   Since a fraction is zero when its numerator is zero (and the denominator is not zero), we set 
   $$
   11x=0 \quad\Longrightarrow\quad x=0.
   $$
   The $$ x $$-intercept is at $$ x=0 $$.

2. **$$ y $$-intercept:**  
   The $$ y $$-intercept is found by evaluating $$ P(x) $$ at $$ x=0 $$:
   $$
   P(0)=\frac{11\cdot 0}{1-0}=0.
   $$
   Thus, the $$ y $$-intercept is at $$ y=0 $$.

In summary:  
- Horizontal asymptotes: There are none.  
- $$ x $$-intercept(s): $$ x=0 $$.  
- $$ y $$-intercept: $$ y=0 $$.
**A. Horizontal Asymptote** There are no horizontal asymptotes. **B. Intercepts** - $$ x $$-intercept: $$ x=0 $$ - $$ y $$-intercept: $$ y=0 $$

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