y=x^3-2x^2-x+2 and y=-x^2+5x+2 To determine:a) Graph of both functions b) At how

For the following exercise, for each polynomial, a. find the degree; b. find the zeros, if any; c. find the y-intercept(s), if any; d. use the leading coefficient to determine the graph’s end behavior; and e. determine algebraically whether the polynomial is even, odd, or neither.
${\displaystyle f\left(x\right)=x^3+3x^2-x-3}$

${\displaystyle f\left(x\right)=x^5+2x^4+3x^3-2x^6-9x^2-6x+4}$
Is it true or false the degree of this polynomial function is 5? If not, why? What is the degree?

Copy and complete the anticipation guide in your notes. StatementThe quadratic formula can only be used when solving a quadratic equation.Cubic equations always have three real roots.The graph of a cubic function always passes through all four quadrants.The graphs of all polynomial functions must pass through at least two quadrants.The expression $x2>4$ is only true if $x>2$.If you know the instantaneous rates of change for a function at $x=2$ and $x=3$, you can predict fairly well what the function looks like in between.
Agree Disagree Justification
Statement
The quadratic formula can only be used when solving a quadratic equation. Cubic equations always have three real roots. The graph of a cubic function always passes through all four quadrants. The graphs of all polynomial functions must pass through at least two quadrants.
The expression $x2>4$ is only true if $x>2$. If you know the instantaneous rates of change for a function at $x=2$ and $x=3$, you can predict fairly well what the function looks like in between.

How does one find the lovely asymptotes of a polynomial graph?

For the following exercises, use the given information about the polynomial graph to write the equation. Double zero at ${\displaystyle x=-3}$ and triple zero ${\displaystyle atx=0}$. Passes through the point (1, 32).

Graph the polynomial function. ${\displaystyle f\left(x\right)=-x^4+3x^3-x+1}$

Find the Taylor polynomial T3(x) for the function f centered at the number a. Graph f and T3 on the same screen.
${\displaystyle f\left(x\right)=x+e^{-x},a=0}$