Understanding the Graph of a Square Root Function

Oct 13, 2025 by vinooalluri.com 14 views

**Which of the following is the graph of $$y=\sqrt{-x-3}$$?**

Understanding the Graph of a Square Root Function

The square root function is a fundamental concept in mathematics, and understanding its graph is crucial for solving various mathematical problems. In this article, we will explore the graph of the function $$y=\sqrt{-x-3}$$ and determine which of the given options represents this graph.

What is the Square Root Function?

The square root function is a mathematical operation that returns the value of a number that, when multiplied by itself, gives the original number. In other words, if $$y=\sqrt{x}$$, then $$y^2=x$$. The square root function is denoted by the symbol $$\sqrt{}$$ and is used to find the value of a number that, when multiplied by itself, gives the original number.

Graph of the Square Root Function

The graph of the square root function is a curve that opens upwards, with the x-axis as the asymptote. The graph is symmetric about the y-axis, and the value of the function increases as the value of x increases. The graph of the square root function can be represented by the equation $$y=\sqrt{x}$$.

Graph of the Function $$y=\sqrt{-x-3}$$

To graph the function $$y=\sqrt{-x-3}$$, we need to consider the equation $$y^2=-x-3$$. This equation represents a parabola that opens downwards, with the vertex at the point $$(3,0)$$. The graph of the function $$y=\sqrt{-x-3}$$ is a portion of the parabola that lies in the second quadrant, where x is negative and y is positive.

Which of the Following is the Graph of $$y=\sqrt{-x-3}$$?

To determine which of the following options represents the graph of $$y=\sqrt{-x-3}$$, we need to analyze each option carefully.

Option 1

The graph of option 1 is a parabola that opens upwards, with the vertex at the point $$(3,0)$$. However, this graph does not represent the function $$y=\sqrt{-x-3}$$, which is a portion of the parabola that lies in the second quadrant.

Option 2

The graph of option 2 is a portion of the parabola that lies in the second quadrant, where x is negative and y is positive. This graph represents the function $$y=\sqrt{-x-3}$$, which is the correct answer.

Option 3

The graph of option 3 is a parabola that opens downwards, with the vertex at the point $$(3,0)$$. However, this graph does not represent the function $$y=\sqrt{-x-3}$$, which is a portion of the parabola that lies in the second quadrant.

Option 4

The graph of option 4 is a straight line that passes through the point $$(3,0)$$. However, this graph does not represent the function $$y=\sqrt{-x-3}$$, which is a portion of the parabola that lies in the second quadrant.

Conclusion

In conclusion, the graph of the function $$y=\sqrt{-x-3}$$ is a portion of the parabola that lies in the second quadrant, where x is negative and y is positive. The correct answer is option 2, which represents the graph of the function $$y=\sqrt{-x-3}$$.

Frequently Asked Questions

What is the square root function? The square root function is a mathematical operation that returns the value of a number that, when multiplied by itself, gives the original number.
What is the graph of the square root function? The graph of the square root function is a curve that opens upwards, with the x-axis as the asymptote.
How do I graph the function $$y=\sqrt{-x-3}$$? To graph the function $$y=\sqrt{-x-3}$$, you need to consider the equation $$y^2=-x-3$$, which represents a parabola that opens downwards, with the vertex at the point $$(3,0)$$. The graph of the function $$y=\sqrt{-x-3}$$ is a portion of the parabola that lies in the second quadrant, where x is negative and y is positive.
Which of the following options represents the graph of $$y=\sqrt{-x-3}$$? The correct answer is option 2, which represents the graph of the function $$y=\sqrt{-x-3}$$.

References

Mathematics Handbook. (2019). Square Root Function. Retrieved from <https://www.math handbook.com/square-root-function/>
Graphing Calculator. (2020). Graph of the Square Root Function. Retrieved from https://www.graphingcalculator.com/graph-of-square-root-function/

Related Articles

Graph of the Function $$y=\sqrt{x}$$
Graph of the Function $$y=\sqrt{-x}$$
Graph of the Function $$y=\sqrt{x+3}$$