a) We must let \(f(x)=0\).
\(3x^3+10x^2-13x-20=0\), and solving we get \(x=-4, -1, \frac{5}{3}\) .
Therefore, the x-intercepts are \(x=-4, -1, \frac{5}{3}\).
b) Let \(x=0\) , and solving we get \(-20\) .
Therefore, the y-intercept is \(y=-20\).
c) This is simple, make a point between \(x=-4\) and \(x=-1\), for example, \((-3, 0)\).
Same for \(x=-1\) and \(x=5/3\) , for example, \((1, 0)\) .
d) As \(x\) goes toward negative infinity, we know that \(x^3\) will always decrease, and vice versa.
e) Your graph may look something like this:
You are very welcome!
:P
