4. Polynomial Functions

In Exercises 33–40, use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x)=x⁵−x³−1; between 1 and 2

In Exercises 15–18, use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. Then use this end behavior to match the polynomial function with its graph. [The graphs are labeled (a) through (d).] <IMAGE>

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

Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. $f\left(x\right)=11x^3-6x^2+x+3$

In Exercises 15–18, use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. Then use this end behavior to match the polynomial function with its graph. [The graphs are labeled (a) through (d).] <IMAGE>

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

Based on the known points plotted on the graph, determine what intervals the graph should be broken into.  

Plotted points are: $\(\left\)(-3,0\(\right\)),$$\(\left\)(0,1\(\right\)),\(\left\)(2,0\(\right\)),$ & $\(\left\)(5,0\(\right\))$

Graph the polynomial function. Determine the domain and range. $f\(\left\)(x\(\right\))=\(\left\)(3x+2\(\right\))\(\left\)(x-1\(\right\))^2$

In Exercises 19–24, use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. $f\left(x\right)=-11x^4-6x^2+x+3$

Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers.f(x)=2x⁴−4x²+1; between -1 and 0

Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. $f\left(x\right)=5x^4+7x^2-x+9$

In Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. g(x)=6x⁷+πx⁵+2/3 x

Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x)=3x³−10x+9; between -3 and -2

In Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. f(x)=x^1/3 −4x²+7