4. Polynomial 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\(\right\))=4x^3+\(\frac\)12x^{-1}-2x+1$

If the given term is the dominating term of a polynomial function, what can we conclude about each of the following features of the graph of the function? (a) domain (b) range (c) end behavior (d) number of zeros (e) number of turning points 10x⁷

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=(3x-1)(x+2)²

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

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

a.b. c. d.

Identify which graphs are not those of polynomial functions.

Match the given polynomial function to its graph based on end behavior. $f\(\left\)(x\(\right\))=-2x^3+x^2+1$

Use a graphing calculator to find the coordinates of the turning points of the graph of each polynomial function in the given domain interval. Give answers to the nearest hundredth. ƒ(x)=2x³-5x²-x+1; [1.4, 2]

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

Use an end behavior diagram, as shown below, to describe the end behavior of the graph of each polynomial function. ƒ(x)=9x⁶-3x⁴+x²-2

Determine the largest open interval of the domain (a) over which the function is increasing and (b) over which it is decreasing. ƒ(x) = -3x² + 18x + 1

Find the zeros for each polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero. f(x)=−3(x+1/2)(x−4)³

Use an end behavior diagram, as shown below, to describe the end behavior of the graph of each polynomial function. ƒ(x)=5x⁵+2x³-3x+4

Use an end behavior diagram, as shown below, to describe the end behavior of the graph of each polynomial function. ƒ(x)=3+2x-4x²-5x¹⁰

If the given term is the dominating term of a polynomial function, what can we conclude about each of the following features of the graph of the function? (a) domain (b) range (c) end behavior (d) number of zeros (e) number of turning points -9x⁶