Reflection of a Square Root Function

Oct 13, 2025 by talynt.org 77 views

**Determine the Graph of a Square Root Function** =====================================================

Reflection of a Square Root Function

What is a Square Root Function?

A square root function is a type of mathematical function that involves the square root of a variable. It is represented by the equation f(x) = √x, where x is the input value and f(x) is the output value. The square root function is an increasing function, meaning that as the input value x increases, the output value f(x) also increases.

Reflection of a Square Root Function over the x-axis

The reflection of a square root function over the x-axis is a new function that is obtained by changing the sign of the output value of the original function. In other words, if we have a function f(x) = √x, then its reflection over the x-axis is given by the function f(x) = -√x.

How to Determine the Reflection of a Square Root Function?

To determine the reflection of a square root function, we need to follow these steps:

Identify the original function: The original function is given by f(x) = √x.
Change the sign of the output value: To obtain the reflection of the function, we need to change the sign of the output value. In this case, we change the sign of √x to -√x.
Write the new function: The new function is given by f(x) = -√x.

Example: Reflection of a Square Root Function

Let's consider an example to illustrate the reflection of a square root function. Suppose we have a function f(x) = √x. To determine its reflection over the x-axis, we need to change the sign of the output value. The new function is given by f(x) = -√x.

Q&A

Q: What is the reflection of a square root function over the x-axis?

A: The reflection of a square root function over the x-axis is a new function that is obtained by changing the sign of the output value of the original function.

Q: How to determine the reflection of a square root function?

A: To determine the reflection of a square root function, we need to follow these steps: identify the original function, change the sign of the output value, and write the new function.

Q: What is the new function obtained by reflecting a square root function over the x-axis?

A: The new function obtained by reflecting a square root function over the x-axis is given by f(x) = -√x.

Q: Is the reflection of a square root function an increasing or decreasing function?

A: The reflection of a square root function is a decreasing function, since the output value decreases as the input value increases.

Q: Can we reflect a square root function over the y-axis?

A: Yes, we can reflect a square root function over the y-axis by changing the sign of the input value.

Q: How to determine the reflection of a square root function over the y-axis?

A: To determine the reflection of a square root function over the y-axis, we need to follow these steps: identify the original function, change the sign of the input value, and write the new function.

Q: What is the new function obtained by reflecting a square root function over the y-axis?

A: The new function obtained by reflecting a square root function over the y-axis is given by f(x) = √(-x).

Q: Is the reflection of a square root function over the y-axis an increasing or decreasing function?

A: The reflection of a square root function over the y-axis is an increasing function, since the output value increases as the input value decreases.

Conclusion

In conclusion, the reflection of a square root function over the x-axis is a new function that is obtained by changing the sign of the output value of the original function. We can determine the reflection of a square root function by following a few simple steps. The reflection of a square root function over the x-axis is a decreasing function, while the reflection of a square root function over the y-axis is an increasing function.

References

[1] "Square Root Function." Math Open Reference, mathopenref.com/square_root_function.html.
[2] "Reflection of a Function." Khan Academy, khanacademy.org/math/algebra/advanced-algebra/reflection-of-a-function.