https://file.aiquickdraw.com/mathbot/file/1726981328057w5iu2xim.jpg

The image shows two rational functions, both the same function, \( f(x) = \frac{-3x}{x-2} \), with instructions to draw the horizontal and vertical asymptotes on separate graphs and write the equations for each asymptote.

Let's address each:

### 1. **Horizontal Asymptote**:
- For rational functions, the horizontal asymptote is determined by comparing the degrees of the numerator and denominator. In this case, the degrees of both the numerator (-3x) and the denominator (x-2) are 1.
- When the degrees are the same, the horizontal asymptote is given by the ratio of the leading coefficients. 
  - Leading coefficient of the numerator: \(-3\)
  - Leading coefficient of the denominator: \(1\)
  - Therefore, the horizontal asymptote is:
  \[
  y = \frac{-3}{1} = -3
  \]

### 2. **Vertical Asymptote**:
- The vertical asymptote occurs where the denominator equals zero, as the function becomes undefined at those points.
  - Set the denominator equal to zero: \(x - 2 = 0\)
  - Solving this gives \(x = 2\).
 

Two copies of the same rational function are shown. The task is to draw the horizontal and vertical asymptotes and write their equations for the function f(x) = (-3x)/(x-2).

Learn how to determine the horizontal and vertical asymptotes for the rational function f(x) = (-3x)/(x-2). This tutorial covers key concepts in algebra and rational functions, suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation