So let's see if we can solve this problem. Below, we have the function \( f(x) \), which is represented by the curve you see or 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, as we have been learning about, and in this situation, what will 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 and folding it. 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. So 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's 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.
0. Review of College Algebra
Transformations
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