Draw the graph of the function f(x)=1÷x,where x≠0.wrote its domain and range

Here is the graph of the function \( f(x) = \frac{1}{x} \). You can observe that:

- The graph consists of two branches, located in the first and third quadrants.
- It has vertical and horizontal asymptotes at \( x = 0 \) and \( y = 0 \), respectively.

### Summary:
- **Domain:** \( x \in (-\infty, 0) \cup (0, +\infty) \)
- **Range:** \( y \in (-\infty, 0) \cup (0, +\infty) \)

Would you like more details or have any questions?

### Related Questions:
1. What are asymptotes, and how are they determined for a given function?
2. How does the graph of \( f(x) = \frac{1}{x} \) compare to \( f(x) = \frac{1}{x^2} \)?
3. What are the transformations of \( f(x) = \frac{1}{x} \) when it is translated or scaled?
4. How can we find the inverse of the function \( f(x) = \frac{1}{x} \), and what does its graph look like?
5. What is the behavior of the function \( f(x) = \frac{1}{x} \) as \( x \to \infty \) or \( x \to -\infty \)?

**Tip:** For functions involving division by zero, always consider the behavior near the undefined points to understand their graph better.

Explore the graph of the function f(x) = 1/x with detailed explanations of its domain, range, and asymptotes. Understand the behavior of the function near its undefined points and its graphical representation. Suitable for high school students studying functions and graphing.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation