3. Polynomial and Rational Functions

Determine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient.

$f\left(x\right)=2+x$

Determine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient.

$f\left(x\right)=3x^2+5x+2$

Based ONLY on the maximum number of turning points, which of the following graphs could NOT be the graph of the given function?

$f\left(x\right)=x^3+1$

Find the zeros of the given polynomial function and give the multiplicity of each. State whether the graph crosses or touches the x-axis at each zero.

$f\left(x\right)=x^2{(x-1)}^3(2x+6)$

Determine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient.

$f\left(x\right)=4x^3+\frac{1}{2}{x}^{-1}-2x+1$

The given term represents the leading term of some polynomial function. Determine the end behavior and the maximum number of turning points.

$4x^5$

Find the zeros of the given polynomial function and give the multiplicity of each. State whether the graph crosses or touches the x-axis at each zero.

$f\left(x\right)=2x^4-12x^3+18x^2$

Determine the end behavior of the given polynomial function.

$f\left(x\right)=x^2+4x+x+7x^3$

Match the given polynomial function to its graph based on end behavior.

$f\left(x\right)=-2x^3+x^2+1$

Determine the maximum number of turning points for the given polynomial function.

$f\left(x\right)=6x^4+2x$