Question
For the polynomial function below; (a) List each real zero and mulliplicity: Determire Whether the Aracn CMda ui loucnu y Ihe K-arie the graph: (d) Determine the end behavior; tha: find the power furcbon Iha: the graph resemb 8? Largc valeseach x Intercept_ (c) Detormine the maxlmum number of tuming points 0nI(x) = (x- 3J*(x+42(a) Find any real zerosSelect Ine correct choice belom=necessarythe answecompleje Vour cnoicaThe real zero(s) of f islare (Type an exaci answer; U3 ng racicals a5 needed U
For the polynomial function below; (a) List each real zero and mulliplicity: Determire Whether the Aracn CMda ui loucnu y Ihe K-arie the graph: (d) Determine the end behavior; tha: find the power furcbon Iha: the graph resemb 8? Largc vales each x Intercept_ (c) Detormine the maxlmum number of tuming points 0n I(x) = (x- 3J*(x+42 (a) Find any real zeros Select Ine correct choice belom= necessary the answe compleje Vour cnoica The real zero(s) of f islare (Type an exaci answer; U3 ng racicals a5 needed Use intugers fracticns for anx nmbers the expression There are rea| zeros: comma separae answen needed ) The multiplicity tne larger zero_ (Type Whole number:) The multipliaity the smal (Type whole number ) (b} The graph the X-axis tne large X-intercepl The graph the *-axis a1 the sma x-intercept; (c) Tne maximum number WWutting points on the graph (d) Type the power function that the graph of f resembles for large values
Answers
For each polynomial function: $$ \begin{array}{l}{\text { (a) List each real zero and its multiplicity. }} \\ {\text { (b) Detemine whether the graph crosses or touches the } x \text { -axis at each } x \text { -interept. }} \\ {\text { (c) Determine the maximum number or tuming points on the graph. }} \\ {\text { (d) Determine the cond behovior, that is, find the power function that the graph of resembles for large values of }|x| \text { . }}\end{array} $$ $$ f(x)=\left(x-\frac{1}{3}\right)^{2}(x-1)^{3} $$
People. A normal given to us is F X is equal toe X minus five whole cubed multiplied with X plus four squared So clearly What we can see is that the polynomial has its riel solutions at X, equal to five, with the multiplicity off three on X equal to minus four. With the multiplicity off to now, we know that when the multiplicity is even then the graph is going to touch the X axis and when it will be, orders went across the X axis. So what? We can conclude us that the graph off the function will across the X axis at X equal to five. Andi touch the X axis at X equal to minus four. Now from the expression off the polynomial function, what we can see is that the degree off the polynomial is five, which means that the number off turning points will be equal toe end minus one, which is equal to five minus one, which will be equal to four. Also, four very large, absolute values off X. The given function will behave like X rays to the bar of five
The polynomial given to us is F X is equal to X plus on the route of three hold squared multiplied with X minus to raise to the part of four Now. Clearly, what we can see is that the given polynomial function will have to really solutions. The 1st 1 will be at minus root tree with a multiplicity off. Two on the 2nd 1 will be at two with the multiplicity at four. Since the multiplicity ease are even, in both case to the graph will not cross the X axis anywhere but touch the X axis. So the graph off the function will that the X axis at X equal toe minus root tree Andi X equal to four now from the given polynomial. What we can conclude about the degree off the polynomial is that it will be off degree six, which means that the number off stoning points will be n minus one, which is six minus one, which is five. Also for very large, absolute values off X. The given function will behave like why is equal to X rays to the bar of six
For the polynomial given to us as FX is equal toe four multiplied with X squared plus one multiplied with X minus two Whole Cube. No, first of all, the first part or the first factor off the polynomial clearly is a non riel solution for the given polynomial, so we'll not consider this as root. So therefore will only consider to as the root so which means that the given polynomial has a real solution at two with a multiplicity off. Three. Which means that the graph off the given polynomial is going toe cross the X axis at X equal to two. Now the degree off the polynomial from the polynomial, we can see that it will be cool toe five, which gives us the number off turning points for the polynomial as n minus one, which is five minus one, which is four now for very large, absolute values affects the polynomial. If affects will behave like that off four X rays to the bar off five
We have been given a polynomial that ffx is equal toe minus two multiplied with X squared plus three whole cute. Now, clearly from the given polynomial. What we can conclude is that it will have no really roots or zeroes or solution as if equipped, X squared, plus three cool to zero. It will give us that X squared is equal to minus three, which means that X is not equal to any real number. And now, since the given polynomial has no real solutions, it means that the graph off the function is not going toe touch or gross the X axis anywhere, also from the polynomial. What we can see is that the degree end off the polynomial is six, which means that the number off turning points for the polynomial will be in minus one, which is six minus one, which is equal to five on for very large absolute values off X. The given polynomial is going to behave likewise equal to minus two X rays to the bar of six