Вопрос:

Analyze the provided image and extract the mathematical formulas and associated graphs.

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Ответ:

Mathematical Formulas and Graphs:

The image displays two graphs, likely representing functions, alongside a section labeled "ФОРМУЛЫ" (FORMULAS) which lists two equations.

Formulas:

  • 1) \( y = -x - 2 \)
  • 2) \( y = \frac{1}{2x} \)

Graphs:

Two coordinate systems are shown, each with a plotted curve. The axes are labeled 'O' for the origin and '1' for the unit mark on both the x and y axes.

  • Graph 1: Appears to be a hyperbola in the second and fourth quadrants, potentially representing an inverse relationship like \( y = \frac{k}{x} \) or a translated version thereof. The curve approaches the x-axis as \( x \to \infty \) and the y-axis as \( y \to \infty \) (and vice-versa for negative values).
  • Graph 2: Also appears to be a hyperbola, but positioned differently. It has branches in the first and third quadrants. The curve approaches the x-axis as \( x \to \infty \) and the y-axis as \( y \to \infty \) (and vice-versa for negative values). This might represent a function like \( y = \frac{k}{x} \) where \( k > 0 \).

Note: Without explicit labels linking each formula to a specific graph, the exact correspondence cannot be determined from the image alone. The visual characteristics of the graphs suggest they are related to inverse proportionality or rational functions.

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