You can put this solution on YOUR website!
If we're given the graph of f(x) and then we replace EVERY x value with its opposite value
, then what simply happens is that the graph will reflect over the y-axis. Why? Think of a number line. Draw it out if you have to. Now let's say that we plotted a bunch of random points on this number line. These points are sort of like the graph. Now negate each point. So a point of x=2 will become x=-2 and something like x=-4 will then become x=4. What you will see happening is that the points will simply reflect over the middle x=0.
If you add another axis (the y-axis), this works the same way. However, this time the points in question are connected by a continuous line or curve.
To answer your question, the graph doesn't shift since you aren't doing any translations. The graph is reflecting over the y-axis.
Here are some examples:
compare that to the graph of
. Note: Just replace every 'x' with '-x'
If we graph the two together, we get
From the last graph, we see that the second graph is simply a reflection of the first one.