Question
Follow the steps for graphing a rational function to graph the function \( R(x)=\frac{x+2}{x(x+9)} \). If needed, first write the given function as a single rational expression. Then, factor the numerator and denominator of \( \mathrm{R}(\mathrm{x}) \). Se complete your choice. A. \( R(x)= \) \( \square \) (Type your answer in factored form. Do not simplify.) B. \( R(x) \) cannot be factored further. What is the domain of \( R(x) \) ? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( \{x \mid x<\square\} \) (Type an integer or a simplified fraction.) B. \( \{x \mid x \neq \square\} \) \( \square \) (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) C. \( \{x \mid x \geq \) \( \square \) \} (Type an integer or a simplified fraction.) D. The domain is the set of all real numbers.
Ask by Bowen Matthews. in the United States
Mar 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
**A.** \( R(x) = \frac{(x+2)}{x(x+9)} \)
**B.** \( \{x \mid x \neq 0,\, x \neq -9\} \)
Solution
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Bonus Knowledge
To write the function \( R(x) = \frac{x+2}{x(x+9)} \) in factored form, we can state: A. \( R(x) = \frac{(x+2)}{x(x+9)} \) Next, we can determine the domain of \( R(x) \). The denominator \( x(x + 9) \) cannot be zero, so we find when each factor equals zero: - \( x = 0 \) - \( x + 9 = 0 \) which simplifies to \( x = -9 \). Thus, the values to exclude from the domain are 0 and -9. B. \( \{x \mid x \neq -9, 0\} \)
