Question 847446
Given {{{y = (x-9)(x+9)^2(9x-6)}}};


1)  Graphing it first, should NOT be done.  Analyze the equation or function first, and then begin a graph sketch.

2)  This is a polynomial function, although in its factored form.  Domain is all real numbers.   Range?  ...?

3)   Let x=0 and solve for y.  That is your y-intercept.  

4)  Zeros and multiplicities?  The function is already factored into binomials; what do you figure?

5)  x to the what power?  That is the degree.

6)  End-behavior is taken from qualitative knowledge about polynomial functions.  Look at what the leading term will be:  9x^4.  Coefficient is positive, and the degree is even.  This means that the left and right unbounded values will increase; and that you can expect some minimums.  You might expect possibly two "trough" forms in the graph.

You are ready to begin sketching the graph.  (I skipped addressing number 7 and 8).  The obvious critical points to check will be {{{x=9}}}, {{{x=-9}}}, and {{{x=2/3}}}.


----I tried to include the graph here, but the display is hard to read---
{{{graph(350,350,-13,12,-35000,40000,(x-9)(x+9)^2(9x-6))}}}