Reflecting functions: examples | Transformations of functions | Algebra 2 | Khan Academy | Summary and Q&A

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July 23, 2019
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Khan Academy
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Reflecting functions: examples | Transformations of functions | Algebra 2 | Khan Academy

TL;DR

The video provides practice examples on reflections of functions, discussing how to graph and find the equations of reflected functions.

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Questions & Answers

Q: How can you graph the function g(x) when it is defined as g(x) = f(-x)?

To graph g(x), you need to reflect the graph of f(x) over the y-axis. Each point on the graph of f(x) will have the same y-value but with the opposite x-value, resulting in the graph of g(x).

Q: What happens when g(x) is defined as the negative of f(x)?

If g(x) = -f(x), the graph of g(x) will be a reflection of f(x) over the x-axis. Each point on the graph of f(x) will have the same x-value but with the opposite y-value, resulting in the graph of g(x).

Q: Can you explain how to find the equation of g(x) when it reflects both over the x-axis and y-axis?

If g(x) = -f(-x), you need to reflect f(-x) over both the x-axis and y-axis. This means that you multiply the entire function f(-x) by -1, resulting in g(x) = -f(-x) as the equation of the reflected function.

Q: How would you find the equation of g(x) when it reflects across the y-axis?

When g(x) reflects across the y-axis, it has the equation g(x) = f(-x). You replace all instances of x in the equation of f(x) with -x to obtain the equation for g(x).

Summary & Key Takeaways

  • The video discusses the reflection of a function f(x) in function g(x) defined as g(x) = f(-x), demonstrating the process of graphing g(x) by reflecting f(x) over the y-axis.

  • Another example is presented where g(x) is defined as the negative of f(x), resulting in a reflection of f(x) over the x-axis.

  • The concept of reflecting a function over both the x-axis and y-axis is explored, where g(x) = -f(-x).

  • The last example involves finding the equation of g(x) by reflecting f(x) across the y-axis.

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