Directions say to differentiate the function. We just learned about the power rule so I'm assuming we can use that but I'm stuck on this one. **Example 14: Function Analysis**Given the function:\[ R(x) = \frac{\sqrt{10}}{x^7} \]This expression represents a rational function where the numerator is a constant, \(\sqrt{10}\), and the denominator is \(x^7\), indicating a seventh-degree polynomial in the denominator. The behavior and properties of \(R(x)\) include:1. **Domain:** The domain of \(R(x)\) includes all real numbers except \(x = 0\), as the function is undefined when \(x = 0\).2. **Asymptotes:** - **Vertical Asymptote:** At \(x = 0\), since the denominator approaches zero, \(R(x)\) approaches infinity or negative infinity. Thus, there is a vertical asymptote at \(x = 0\). - **Horizontal Asymptote:** As \(x\) approaches infinity or negative infinity, \(R(x)\) tends to zero because the degree of \(x\) in the denominator is greater than that of the numerator.3. **End Behavior:** As \(x\) increases or decreases without bound, \(R(x)\) approaches zero.**Discussion and Analysis:**This function showcases how polynomial powers in the denominator dominate the behavior of a function, influencing its domain and asymptotic behavior. Understanding these properties can help in sketching the graph of the function and predicting its behavior under various transformations.

Name: Directions say to differentiate the function. We just learned about th
Uploaded: 2024-03-20T06:47:22.000Z
Channel: Bartleby
Description: Directions say to differentiate the function. We just learned about the power rule so I'm assuming we can use that but I'm stuck on this one. **Example 14: Function Analysis**Given the function:\[ R(x) = \frac{\sqrt{10}}{x^7} \]This expression repres