Part ADescribe the type of function shown in the graph.Part BWhat are the standard form and the factored form of the function?

Answer:A[tex]F(x)=-\frac{1}{1500}(x+20)(x+5)(x-15)[/tex]B[tex]=> F(x)=-\frac{x^3}{1500}-\frac{x^2}{150}+\frac{11x}{60}+1[/tex]Step-by-step explanation:Function and its graphs Part A The graph shown in the image corresponds to a cubic function because of its classical infinite branches, three real roots and two extrema values Part B Knowing the value of the three roots x=-20, x=-5, and x=15 we can express the cubic function in factored form: [tex]F(x)=C(x+20)(x+5)(x-15)[/tex]The value of C will be determined by using any particular point from the graph. Let's use (0,1) [tex]1=C(0+20)(0+5)(0-15)[/tex][tex]C=-\frac{1}{1500}[/tex]Replacing, we find the factored form of the function [tex]F(x)=-\frac{1}{1500}(x+20)(x+5)(x-15)[/tex]The standard form demands to expand all the products and simplify [tex]F(x)=-\frac{1}{1500}(x^3+10x^2-275x-1500)[/tex][tex]=> F(x)=-\frac{x^3}{1500}-\frac{x^2}{150}+\frac{11x}{60}+1[/tex]