4 months ago
Q:

What is the end behavior of the graph of fx=x5-8x4+16x3 ? fxto - ∈ fty asxto - ∈ fty ;fxto - ∈ fty asxto + ∈ fty fxto - ∈ fty asxto - ∈ fty ;fxto + ∈ fty asxto + ∈ fty fxto + ∈ fty asxto - ∈ fty ;fxto - ∈ fty asxto + ∈ fty fxto + ∈ fty asxto - ∈ fty ;fxto + ∈ fty asxto + ∈ fty COMPLETE The graph touches, but does not cross, the x--axis at x=square The graph of the function crosses the x--axis at x=square . DONE

What is the end behavior of the graph of fx=x5-8x4+16x3 ? fxto - ∈ fty asxto - ∈ fty ;fxto - ∈ fty asxto + ∈ fty fxto - ∈ fty asxto - ∈ fty ;fxto + ∈ fty asxto + ∈ fty fxto + ∈ fty asxto - ∈ fty ;fxto - ∈ fty asxto + ∈ fty fxto + ∈ fty asxto - ∈ fty ;fxto + ∈ fty asxto + ∈ fty COMPLETE The graph touches, but does not cross, the x--axis at x=square The graph of the function crosses the x--axis at x=square . DONE

Accepted Solution

A:
Determine x intercept(s) bounce/cross the x-axis:: x = 4, bounce, x = 0, crossAnalyze end behavior of f{(x )} = x^{5} - 8 x^{4} + 16 x^{3}:: as x →\infty，f(x)→ \infty; as x →-\infty，f(x)→ -\inftyThe graph of f(x) = x^{5}-8x^{4}+16x^{3} ::