Can someone please explain this to me fan and medal

Describe the graph of the function f(x) = x3 − 18x2 + 107x − 210. Include the y-intercept, x-intercepts, and the shape of the graph.

If I am correct, I know the x-intercepts are (5,0), (6,0) and (7,0). I don't know the y-intercept or the shape of the graph.

Question

Can someone please explain this to me fan and medal



Describe the graph of the function f(x) = x3 − 18x2 + 107x − 210. Include the y-intercept, x-intercepts, and the shape of the graph.


If I am correct, I know the x-intercepts are (5,0), (6,0) and (7,0).   I don't know the y-intercept or the shape of the graph.

tkhunny · Answer

1) I didn't check the x-intercepts.  They look reasonable.
2) y-intercept is trivial.  Substitute x = 0 and immediately, f(x) = -210.
3) Cubics all have the same sort of end behavior.  That x^3 term eventually takes over everything else.  What does g(x) = x^3 do?