Question

NO LINKS!!!

Answer 1

Factor x^5 - x to get x(x^4 - 1) = x(x^2-1)(x^2+1) = x(x-1)(x+1)(x^2+1)

We see that x = 0, x = 1 and  x = -1 are the real number roots or x intercepts. Ignore the complex or imaginary roots. Unfortunately, the graph shows the x intercepts as -2, 0 and 2 which don't match up.

So there's no way that the given graph matches with f(x) = x^5-x.

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As more proof, let's consider the end behavior.

As x gets really large toward positive infinity, x^5 will do the same and so will x^5-x. Overall, f(x) will head off to positive infinity. Visually, moving to the right will have the graph move upward forever. This is the complete opposite of what is shown on the graph.

Likewise, the left endpoint should be aimed down instead of up. This is because x^5-x will approach negative infinity as x heads to the left.

In short, the graph shows a "rises to the left, falls to the right" end behavior. It should show a "falls to the left, rises to the right" pattern if we wanted to have a chance at matching it with x^5-x. Keep in mind that matching end behavior isn't enough to get a 100% match; however, having this contradictory end behavior is proof we can rule out a match.

I recommend using Desmos, GeoGebra, or whatever graphing program you prefer to plot out y = x^5-x. You'll get a bettter idea of what's happening.

Answer 2

Answer:

The answer it attached below :)

Sorry it took so long!