It looks like you're trying to define a function \( f(x) = \frac{4}{x} - 5 \). 

This is a rational function where:

- \( f(x) = \frac{4}{x} - 5 \)
- The first term \( \frac{4}{x} \) represents a rational part, and the second term \( -5 \) is a constant.

### Domain:
- The function is undefined when \( x = 0 \), as division by zero is not possible.

Thus, the domain of the function is all real numbers except \( x = 0 \), or \( x \in (-\infty, 0) \cup (0, \infty) \).

Would you like further details on how to analyze or graph this function? Or perhaps more on domain and range?

### Follow-up questions:
1. What is the domain and range of this function?
2. How do you graph rational functions like this one?
3. What are the vertical and horizontal asymptotes of this function?
4. How does the constant \( -5 \) affect the graph of the function?
5. How can you find the x- and y-intercepts for this function?

**Tip**: The horizontal asymptote of a rational function helps you understand its end behavior for very large values of \(x\).

Explore the rational function f(x) = 4/x - 5, learn how to determine its domain, range, and identify vertical and horizontal asymptotes. This solution is perfect for high school students in Grades 10-12, covering key concepts in algebra.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation