Graph of y -√x: Understanding Its Behavior and Characteristics

The graph of y -√x is a fascinating mathematical function. Unlike the standard square root function, this function exhibits a different behavior, reflecting the concept of a negative square root. Let's delve into its characteristics and graph it using some key steps and a table of points.

Graphical Behavior

The graph of y -√x is a reflection of the graph of y √x across the x-axis. This reflection causes the function to behave differently, creating a downward-facing curve that opens towards negative infinity as x increases. It starts at the origin (0, 0) and continuously decreases as x increases, approaching negative infinity.

Table of Points

To better understand and plot the graph, we can use a table of points where x is a perfect square. Here's a table for x values 0, 1, 4, 9, 16, and 25:

xy 00 1-1 4-2 9-3 16-4 25-5

Using these points, we can connect them to form the graph of y -√x. If we use more points, the graph becomes smoother and more accurate.

Visual Representation

Here is a visual representation of the graph using the points we calculated:

Graph of y -√x

The graph starts at (0, 0) and then decreases as x increases, approaching negative infinity. As x approaches 0, y also approaches 0, but in a negative direction.

Additional Resources

Google and Desmos are powerful tools for visualizing and understanding mathematical functions. To see the graph of y -√x visually, simply search y -sqrt(x) on Google. Alternatively, you can use Desmos to explore this function in more detail. Many textbooks also provide examples and exercises that can help you better understand the graph of this function.

Summary

The graph of y -√x is a reflection of the graph of y √x across the x-axis, making it a downward-opening parabola that starts at the origin and decreases as x increases, approaching negative infinity. By plotting key points, you can form a more accurate and visually intuitive representation of the function.