4. Polynomial Functions

Graph each function. Determine the largest open intervals of the domain over which each function is (a) increasing or (b) decreasing. ƒ(x)=(1/2)(x-2)²+4

For each polynomial function, identify its graph from choices A–F. ƒ(x)=-(x-2)(x-5)

Determine which functions are polynomial functions. For those that are, identify the degree. $f\left(x\right)=(x^2+7)/x^3$

Determine if the given function is a polynomial function. If so, write in standard form, then state the degree and leading coefficient. $f\left(x\right)=4x^3+\frac12x^{-1}-2x+1$

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

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. $f\left(x\right)=-2x^3+x^2+1$

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. $f\left(x\right)=2x^4-12x^3+18x^2$

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

Determine the maximum number of turning points for the given polynomial function. $f\left(x\right)=6x^4+2x$

Based ONLY on the maximum number of turning points, which of the following graphs could NOT be the graph of the given function? $f\left(x\right)=x^3+1$

The given term represents the leading term of some polynomial function. Determine the end behavior and the maximum number of turning points. $4x^5$