Graph the polynomial $f(x)=x^4-3x^3-4x^2+3x-2$ using a graphing calculator Graph the polynomial $f(x)=x^4-3x^3-4x^2+3x-2$ using a graphing calculator? 
a) The Range
b) The Real Zeros
c) The y-intercept
d) relative minimum and Relative Maximum
e) The interval where $f(x)\le0$

With the help of the calculator is easy to establish:
$$
   \begin{array}{c|ccccc} a & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 \\ \hline \\ f(a) & 115 & 16 & -5 & -2 &-5 & -20 & -29 & 10\end{array}
$$
This suggests the minimum is close to $-29$. In fact it is $-29.4136$. For very large $|x|$, the fourth power will dominate other terms, therefore the polynomial grows boundlessly for large $|x|$. Thus the range is $(-29.4136, \infty)$.
The tabulation indicates that real zeros are in the intervals $(-2,-1)$ and $(3,4)$. In fact, using calculator (or W|A) you could establish that
$$
   x^4 -3 x^3 - 4x^2+3x-2 = \left(x-\frac{3}{4} \right)^4 - \frac{59}{8} \left(x-\frac{75}{236} \right)^2 - \frac{23737}{15104}
$$
which shows that these are the only real roots, and the polynomial is negative in between them. Approximate values of these roots are $-1.5163$ and $3.86814$
