Find the horizontal and verlical asymptotes of .

Find the horizontal asymptotes. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice
A. The function has one horizontal asymptote,
(Type an equation.)
B. The function has two horizontal asymptotes. The top asymptote is and the bottom asymptote is
(Type equations.)
C. The function has no horizontal asymptotes.

Ask by Lang Rogers. in the United States

Jan 22,2025

Question

Find the horizontal and verlical asymptotes of .

Find the horizontal asymptotes. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice
A. The function has one horizontal asymptote,
(Type an equation.)
B. The function has two horizontal asymptotes. The top asymptote is and the bottom asymptote is
(Type equations.)
C. The function has no horizontal asymptotes.

Ask by Lang Rogers. in the United States

Jan 22,2025

UpStudy AI · Accepted Answer

To determine the horizontal asymptotes of the function $$ f(x) = \frac{7x}{x + 4} $$, we'll analyze the degrees of the numerator and the denominator.

1. **Degrees of the Polynomial:**
   - **Numerator ($$7x$$)**: Degree 1
   - **Denominator ($$x + 4$$)**: Degree 1

2. **Determining the Horizontal Asymptote:**
   - When the degrees of the numerator and the denominator are **equal**, the horizontal asymptote is the ratio of the leading coefficients.
   - **Leading Coefficient of Numerator**: 7
   - **Leading Coefficient of Denominator**: 1

Therefore, the horizontal asymptote is:
   $$
   y = \frac{7}{1} = 7
   $$

**Conclusion:**

**Choice A** is correct.

**A.** The function has one horizontal asymptote, $$ y = 7 $$.
The function has one horizontal asymptote, $$ y = 7 $$.

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