Math Problem Statement

What the correct answer

What is the solution to the function h(x) = 2/x?

Solution

The image shows the function h(x)=2xh(x) = \frac{2}{x}.

It appears you're looking to solve or analyze something about this function. Since it's an expression for a rational function, here are a few potential directions you could explore:

  1. Domain: The domain of h(x)=2xh(x) = \frac{2}{x} is all real numbers except x=0x = 0, because division by zero is undefined.

  2. Range: The range of this function includes all real numbers except zero. Since the numerator is a constant (2), the function will never output 0.

  3. Asymptotes:

    • Vertical asymptote: At x=0x = 0, the function has a vertical asymptote, as the function tends toward infinity as xx approaches 0.
    • Horizontal asymptote: As xx approaches either positive or negative infinity, h(x)h(x) approaches 0.
  4. Graph behavior: The graph of h(x)=2xh(x) = \frac{2}{x} is a hyperbola, with two distinct branches: one in the first quadrant for positive xx values and one in the third quadrant for negative xx values.

If you were seeking a specific solution or analysis, feel free to clarify. Would you like to explore one of these concepts further, or do you have another type of question about this function?

Here are five related questions:

  1. What are the intercepts of the function h(x)=2xh(x) = \frac{2}{x}?
  2. How does the function behave as x0+x \to 0^+ and x0x \to 0^-?
  3. Can we find the inverse of the function h(x)=2xh(x) = \frac{2}{x}?
  4. What is the derivative of h(x)h(x) with respect to xx?
  5. How can we determine the concavity of the graph for h(x)=2xh(x) = \frac{2}{x}?

Tip: For rational functions like this, identifying the vertical and horizontal asymptotes gives a good sense of how the function behaves for large and small xx values.

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Math Problem Analysis

Mathematical Concepts

Algebra
Rational Functions
Asymptotes

Formulas

h(x) = 2/x

Theorems

Vertical Asymptote
Horizontal Asymptote

Suitable Grade Level

Grades 9-12