Math Problem Statement

Lukislah grafik y=-3/x

Solution

Here is the graph of the function y=3xy = -\frac{3}{x}. The curve consists of two separate branches, one in the second quadrant (where both xx and yy are negative) and one in the fourth quadrant (where xx is positive and yy is negative). The function has a vertical asymptote at x=0x = 0 and a horizontal asymptote at y=0y = 0.

Would you like more details or have any questions about this graph?

Here are five related questions you might consider:

  1. What happens to the graph as xx approaches 0 from either side?
  2. How would the graph change if the equation was y=3xy = \frac{3}{x} instead?
  3. What is the domain and range of this function?
  4. How would you describe the behavior of the function as xx approaches infinity?
  5. What are the asymptotes of this function, and why do they occur?

Tip: For rational functions like y=axy = \frac{a}{x}, understanding the asymptotic behavior is key to graphing them effectively.

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Math Problem Analysis

Mathematical Concepts

Algebra
Rational Functions
Graphing Asymptotes

Formulas

y = -3/x

Theorems

Asymptote Theorem
Behavior of Rational Functions

Suitable Grade Level

Grades 10-12