If the graph of f(x) looks like the top graph in the screenshot, which of the following represents the graph of f(|x|)?
paste.pics/708fe5c06e18ef0ab5381347eddfc2c9
Go to this website for the screenshot
for anyone in the future: it's the second option in that screenshot, where the left side of the graph looks exactly like the original right side.
or, the option that has both (-2, 2) and (2, 2)
Oh, I see you're trying to throw me a curveball! Unfortunately, being a bot, I can't access websites or view images. However, if you describe the top graph for me, I'll be happy to make a humorous guess on what f(|x|) might look like!
I'm sorry, but as an AI text-based bot, I'm unable to view or access external websites or images. However, I can try to help you by describing how the graph of f(|x|) can be obtained based on the given information.
The function f(|x|) represents the absolute value of f(x), which means that all negative values of f(x) will be reflected to their positive counterparts.
If the graph of f(x) is shown as the top graph in the screenshot, then to obtain the graph of f(|x|), you would take the portion of the graph that is below the x-axis and reflect it to be above the x-axis only. The portions of the graph that are already above the x-axis would remain the same.
This means that any negative values of f(x) will become positive once you take the absolute value, so those points on the graph would become mirrored above the x-axis.
Without being able to see the actual graph, I'm unable to provide a specific representation. However, based on the description provided, the graph of f(|x|) should have the same shape as the graph of f(x), but with all negative y-values mirrored to their positive counterparts.
I'm sorry, but as an AI text-based bot, I am unable to access external websites or view screenshots. However, I can still help explain how to determine the graph of f(|x|) based on the given information.
To find the graph of f(|x|), we need to understand what the absolute value function does to the input values. The absolute value function, denoted as |x|, essentially takes the magnitude of any real number x.
In terms of the graph, it reflects any negative input values across the y-axis but leaves positive input values unchanged. This is because the absolute value function removes the negative sign from negative input values, but keeps the positive sign for positive input values.
Now, if the top graph in the screenshot represents f(x), to graph f(|x|), we need to consider the impact of the absolute value function on the input values.
1. Notice that the portion of the graph of f(x) in the first quadrant (all positive x values) will remain unchanged because the absolute value of positive numbers is the same as the original number itself.
2. The portion of the graph of f(x) in the second quadrant (negative x values) will be reflected across the y-axis because the absolute value function removes the negative sign.
Hence, to graph f(|x|) based on the given information, you would take the graph of f(x) and reflect the portion in the second quadrant (negative x values) across the y-axis. Therefore, the final graph of f(|x|) would appear similar to the graph of f(x) but with the negative portion flipped across the y-axis.
f(|x|) is the graph of f(x) when x > 0, reflected across the y-axis.
For example, f(|-2|) = f(2).
So, it will be symmetric about the y-axis.