Solve the polynomial inequality graphically. x^{3}-x^{2}-2xgeq0

Rational functions can have any polynomial in the numerator and denominator. Analyse the key features of each function and sketch its graph. Describe the common features of the graphs.

${\displaystyle a)f\left(x\right)=\frac{x}{x^2-1}}$

$b)g\left(x\right)=\frac{x-2}{x^2+3x+2}$

$c)h\left(x\right)=\frac{x+5}{x^2-x-12}$

Consider the polynomial function ${\displaystyle g\left(x\right)=-x^5-9x^3-8x.}$ Factor $g(x)$ completely and determine all of its complex zeros. Which of the zeros of g are not x-intercepts of the graph of ${\displaystyle y=g\left(x\right)?}$ Why do these zeros not correspond to a point on the x-axis? In general, what can be said about the similarities and differences between the zeros and the x-intercepts of the graphs of polynomial functions?

For the following exercises, use the given information about the polynomial graph to write the equation. Degree 3. Zeros at x = −5, x = −2, and x = 1. y-intercept at (0, 6)

Graph the polynomial function.
${\displaystyle f\left(x\right)=x^5+x^2-4}$

For the following exercises, use the given information about the polynomial graph to write the equation. Degree 5. Double zero at x = 1, and triple zero at x = 3. Passes through the point (2, 15).

Graph the polynomial by transforming an appropriate graph of the form ${\displaystyle y=x^n}$.
Show clearly all x- and y-intercepts. ${\displaystyle P\left(x\right)=-x^3+64}$

Graph each polynomial function. $f(x)=2x^3-x^2+2x-1$