Question

How do you use end behavior, zeros, y intercepts to sketch the graph of `g(x)=1/10(x-2)^3(x+3)^2`?

Answer 1

I like to take advantage of the factored form of the equation:
x - 2 means that x = 2 will be a zero
x+3 means that x = -3 will be a zero

Explanation:

The odd powered term `(x-2)^3` will cause the graph to cross THROUGH the x-axis.
The even powered term `(x+3)^2` will be a location where the graph will be TANGENT to the x-axis. Some describe this as "touching and turning around" at that point.

The total degree is 2 + 3 or 5. An odd total degree , with lead coefficient `1/10` (positive number) will have end behavior that rises to the right and falls to the left.