How do you sketch the general shape of #f(x)=-x^3-6x^2-9x-4# using end behavior?
You need both the solutions and the end behavior to sketch this graph well. There are two solutions at
Because the highest variable (aka the "degree" of the function) is odd, the ends of the graph go in opposite directions.
Think about the cubic parent function, where the right side goes up; the left side goes down; and there's a little wiggle at the origin. It's the same idea with all odd functions: the ends go in opposite directions, and there are wiggles in between.
Now, since the
I used the rational roots test to find that
I used synthetic division to factor it further, and I got
Factoring the quadratic gives you
Since we have two solutions at
Give this information, you can sketch the part of the graph going up and left from
The graph passes through the y axis where