So let's see if we can solve this problem. Below, we have the function f(x), which is the curve you see, represented by the green dotted lines. We are asked to sketch a graph of g(x) where g(x) is the function f(x) after it has been reflected over the x-axis. This is a reflection transformation that we have been learning about. In this situation, what's going to happen is that we will have our graph reflected over the x-axis. When this happens, recall that reflecting over the x-axis is like taking the entire graph like a sheet of paper, creasing it at the x-axis and folding it down. So, if you were to take this portion of the graph and fold it down over the x-axis, the graph would end up looking something like this. This is what your graph is going to look like, where you can literally imagine that this whole thing just gets flipped down and folded over like a sheet of paper. Now, this portion of the graph is going to fold up because it is like folding up over the x-axis. Again, you are creasing this like a piece of paper, so this graph is going to look something like that. Once we have reflected over the x-axis, this is what the new function g(x) is going to look like with respect to our original function f(x), this green dotted curve. This is how you can solve the problem. Hope you found this helpful.
Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
3. Functions
Transformations
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Transformations practice set
