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Describe the graph of \( y=-2 \) * Increasing Decreasing Constant

Ask by Clarke Warren. in the United States
Feb 03,2025

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The graph of \( y = -2 \) is a horizontal line that stays at \( y = -2 \) for all values of \( x \). It is neither increasing nor decreasing; it is constant.

Solución

The equation \( y = -2 \) represents a **constant function**. Here's a detailed description: ### Graph Description: - **Type of Graph:** Horizontal Line - **Position:** The line is parallel to the x-axis and crosses the y-axis at \( y = -2 \). - **Slope:** The slope of the line is 0, indicating no rise or fall as you move along the line. ### Characteristics: - **Constant:** Since \( y \) is always \(-2\) regardless of the value of \( x \), the function does not change; hence, it is constant. - **Increasing/Decreasing:** The function is neither increasing nor decreasing because the value of \( y \) remains the same for all \( x \). ### Visual Representation: ![Graph of y = -2](https://i.imgur.com/uCwucAE.png) In the graph above: - The horizontal line at \( y = -2 \) extends infinitely in both the positive and negative directions along the x-axis. - No matter where you choose a point on this line, the y-coordinate will always be \(-2\). ### Summary: - **Increasing:** No - **Decreasing:** No - **Constant:** Yes The graph of \( y = -2 \) is a **constant function** represented by a horizontal line at \( y = -2 \).

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Mind Expander

Imagine a perfectly straight line horizontally slicing through the y-axis at -2. No matter where you are on the x-axis, whether you're zooming to the left or darting to the right, the value of y remains constantly -2. This means that the graph depicts a constant relationship, showing no rise or fall—just a steady and unwavering course! Now, think about how useful that is in the real world! Such a line can represent things like a fixed budget (spending exactly $2 under your limit) or stable temperature in a controlled environment (like a refrigerator!). Whenever you want something to remain unchanged, there's your trusty constant line, always there if you need it!

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