In calculus, it can be shown that the arctangent function can be approximated by the polynomial arctan x approx x-x^{3}/3+x^{5}/5-x^{7}/7 where x is i

For the following exercises, use the given information about the polynomial graph to write the equation. Degree 4. Root of multiplicity 2 at x = 4, and roots of multiplicity 1 at x = 1 and x = −2. y-intercept at (0, −3).

Suppose f has period 2 and f(x) = x for $0\le x<2$. Find the fourth-degree Fourier polynomial and graph it on $0\le x<2$

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

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

Solve the polynomial inequality graphically. ${\displaystyle 2x^3-5x^2-x+6>0}$

a) Identify the parameters a, k, d, and c in the polynomial function ${\displaystyle y=\frac{1}{3}{[-2(x+3)]}^4-1}$. Describe how each parameter transforms the base function ${\displaystyle y=x^4}$. b) State the domain and range, the vertex, and the equation of the axis of symmetry of the transformed function. c) Describe two possible orders in which the transformations can be applied to the graph of ${\displaystyle y=x^4}$ to produce the graph of ${\displaystyle y=\frac{1}{3}{[-2(x+3)]}^4-1}$. d) Sketch graphs of the base function and the transformed function on the same set of axes.