Understanding the Reflections

Oct 13, 2025 by windailys.com 99 views

**The Graph of $$f(x)=\sqrt{x}$$: Reflections and Transformations**

Understanding the Reflections

The graph of a function can be transformed in various ways, including reflections across the x-axis and y-axis. In this article, we will explore the reflection of the graph of $$f(x)=\sqrt{x}$$ across the x-axis and y-axis to create the graph of function $$g(x)$$.

Reflection Across the x-axis

When a graph is reflected across the x-axis, the y-coordinates of the points on the graph are negated. This means that if a point (a, b) is on the original graph, the corresponding point on the reflected graph will be (a, -b).

Reflection Across the y-axis

When a graph is reflected across the y-axis, the x-coordinates of the points on the graph are negated. This means that if a point (a, b) is on the original graph, the corresponding point on the reflected graph will be (-a, b).

Reflection of $$f(x)=\sqrt{x}$$ Across the x-axis

To reflect the graph of $$f(x)=\sqrt{x}$$ across the x-axis, we need to negate the y-coordinates of the points on the graph. This can be represented by the function $$f(x)=-\sqrt{x}$$.

Reflection of $$f(x)=\sqrt{x}$$ Across the y-axis

To reflect the graph of $$f(x)=\sqrt{x}$$ across the y-axis, we need to negate the x-coordinates of the points on the graph. This can be represented by the function $$f(-x)=\sqrt{-x}$$.

Reflection of $$f(x)=\sqrt{x}$$ Across the x-axis and y-axis

To reflect the graph of $$f(x)=\sqrt{x}$$ across both the x-axis and y-axis, we need to negate both the x-coordinates and y-coordinates of the points on the graph. This can be represented by the function $$f(-x)=-\sqrt{-x}$$.

Q&A

Q: What is the effect of reflecting a graph across the x-axis? A: When a graph is reflected across the x-axis, the y-coordinates of the points on the graph are negated.

Q: What is the effect of reflecting a graph across the y-axis? A: When a graph is reflected across the y-axis, the x-coordinates of the points on the graph are negated.

**Q: How do you reflect the graph of $$f(x)=\sqrtx}$$ across the x-axis?** A To reflect the graph of $$f(x)=\sqrt{x$$ across the x-axis, we need to negate the y-coordinates of the points on the graph. This can be represented by the function $$f(x)=-\sqrt{x}$$.

**Q: How do you reflect the graph of $$f(x)=\sqrtx}$$ across the y-axis?** A To reflect the graph of $$f(x)=\sqrt{x$$ across the y-axis, we need to negate the x-coordinates of the points on the graph. This can be represented by the function $$f(-x)=\sqrt{-x}$$.

**Q: How do you reflect the graph of $$f(x)=\sqrtx}$$ across both the x-axis and y-axis?** A To reflect the graph of $$f(x)=\sqrt{x$$ across both the x-axis and y-axis, we need to negate both the x-coordinates and y-coordinates of the points on the graph. This can be represented by the function $$f(-x)=-\sqrt{-x}$$.

Conclusion

In this article, we have explored the reflection of the graph of $$f(x)=\sqrt{x}$$ across the x-axis and y-axis to create the graph of function $$g(x)$$. We have also answered some common questions about reflecting graphs across the x-axis and y-axis.

Key Takeaways

Reflection across the x-axis negates the y-coordinates of the points on the graph.
Reflection across the y-axis negates the x-coordinates of the points on the graph.
Reflection across both the x-axis and y-axis negates both the x-coordinates and y-coordinates of the points on the graph.

Further Reading

Graph transformations
Reflections in mathematics
Functions and their graphs

References

[1] "Graph Transformations" by Math Open Reference
[2] "Reflections in Mathematics" by Khan Academy
[3] "Functions and Their Graphs" by Wolfram MathWorld