Find \[$ G(x) \$\], Where \[$ G(x) \$\] Is The Reflection Across The \[$ X \$\]-axis Of \[$ F(x) = -6x + 6 \$\].A. \[$ G(x) = 6x + 6 \$\]B. \[$ G(x) = -6x + 6 \$\]C. \[$ G(x) = 6x - 6 \$\]D.
Reflection Across the x-axis: Finding g(x)
Understanding Reflection Across the x-axis
When a function is reflected across the x-axis, the y-values of the function are negated. This means that if we have a function f(x) = y, the reflection of f(x) across the x-axis will be g(x) = -y.
Given Function: f(x) = -6x + 6
The given function is f(x) = -6x + 6. To find the reflection of this function across the x-axis, we need to negate the y-values of the function.
Finding g(x)
To find g(x), we need to negate the y-values of f(x). This means that we need to multiply the entire function by -1.
g(x) = -(-6x + 6)
Using the distributive property, we can simplify this expression:
g(x) = 6x - 6
Comparing g(x) with the Options
Now that we have found g(x), we can compare it with the options given:
A. g(x) = 6x + 6 B. g(x) = -6x + 6 C. g(x) = 6x - 6 D. (no option)
Comparing g(x) = 6x - 6 with the options, we can see that option C is the correct answer.
Conclusion
In this article, we learned how to find the reflection of a function across the x-axis. We used the given function f(x) = -6x + 6 and found its reflection g(x) = 6x - 6. We compared g(x) with the options given and found that option C is the correct answer.
Reflection Across the x-axis: Key Takeaways
- When a function is reflected across the x-axis, the y-values of the function are negated.
- To find the reflection of a function across the x-axis, we need to multiply the entire function by -1.
- The reflection of f(x) = -6x + 6 across the x-axis is g(x) = 6x - 6.
Reflection Across the x-axis: Examples and Exercises
- Find the reflection of f(x) = 2x - 3 across the x-axis.
- Find the reflection of f(x) = x^2 + 1 across the x-axis.
- Find the reflection of f(x) = -x + 2 across the x-axis.
Reflection Across the x-axis: Real-World Applications
- Reflection across the x-axis is used in various real-world applications, such as:
- Physics: to describe the motion of objects
- Engineering: to design and analyze systems
- Computer Science: to develop algorithms and models
Reflection Across the x-axis: Conclusion
In conclusion, reflection across the x-axis is an important concept in mathematics that has various real-world applications. We learned how to find the reflection of a function across the x-axis and compared it with the options given. We also discussed the key takeaways and provided examples and exercises for further practice.
Reflection Across the x-axis: Q&A
Frequently Asked Questions
In this article, we will answer some frequently asked questions about reflection across the x-axis.
Q: What is reflection across the x-axis?
A: Reflection across the x-axis is a transformation that flips a function over the x-axis. This means that the y-values of the function are negated.
Q: How do I find the reflection of a function across the x-axis?
A: To find the reflection of a function across the x-axis, you need to multiply the entire function by -1.
Q: What is the difference between reflection across the x-axis and reflection across the y-axis?
A: Reflection across the x-axis flips a function over the x-axis, while reflection across the y-axis flips a function over the y-axis. This means that the x-values of the function are negated in reflection across the y-axis.
Q: Can I reflect a function across the x-axis multiple times?
A: Yes, you can reflect a function across the x-axis multiple times. Each reflection will flip the function over the x-axis.
Q: How do I graph a function that has been reflected across the x-axis?
A: To graph a function that has been reflected across the x-axis, you need to reflect the original graph over the x-axis. This means that the y-values of the original graph are negated.
Q: Can I reflect a function across the x-axis and then shift it horizontally?
A: Yes, you can reflect a function across the x-axis and then shift it horizontally. This means that you need to reflect the function over the x-axis and then add or subtract a value from the x-values of the function.
Q: How do I find the reflection of a function across the x-axis using a graphing calculator?
A: To find the reflection of a function across the x-axis using a graphing calculator, you need to enter the function and then use the "reflect" or "flip" function to reflect the graph over the x-axis.
Q: Can I reflect a function across the x-axis and then scale it vertically?
A: Yes, you can reflect a function across the x-axis and then scale it vertically. This means that you need to reflect the function over the x-axis and then multiply the y-values of the function by a value.
Q: How do I find the reflection of a function across the x-axis using a computer algebra system?
A: To find the reflection of a function across the x-axis using a computer algebra system, you need to enter the function and then use the "reflect" or "flip" function to reflect the function over the x-axis.
Reflection Across the x-axis: Key Takeaways
- Reflection across the x-axis is a transformation that flips a function over the x-axis.
- To find the reflection of a function across the x-axis, you need to multiply the entire function by -1.
- Reflection across the x-axis can be used to graph functions and to solve problems in mathematics and science.
Reflection Across the x-axis: Real-World Applications
- Reflection across the x-axis is used in various real-world applications, such as:
- Physics: to describe the motion of objects
- Engineering: to design and analyze systems
- Computer Science: to develop algorithms and models
Reflection Across the x-axis: Conclusion
In conclusion, reflection across the x-axis is an important concept in mathematics that has various real-world applications. We answered some frequently asked questions about reflection across the x-axis and provided key takeaways and real-world applications.