Which of the following graphs could be the graph of the function f(x)=0.03x2(x2-25)?

Accepted Solution

Answer:The fourth graph (see attachment)Step-by-step explanation:The function [tex]f(x)=0.03x^2\times{(x^2-25)}[/tex] represents a polinomial of grade 4, which means that it has four roots. The roots of a function are those values that make the function equal to zero. In this particular case, the function f(x) equals zero [tex]0.03x^2\times{(x^2-25)}\\[/tex]=0 in two cases: 1) When the term [tex]0.03x^2=0[/tex], which only happens if x=0; or 2) when [tex](x^2-25)=0[/tex], which can happend if x=5 or if x=-5 (because the product of two negative numbers is possitive).Then, the function graph must show that, f(x) passes trough zero when x=0 (first case) or when x=5 or x=-5 (second case).The only graph that shows that is the one indicated.To verify that the function is well depicted, you can replace any specific value of x (for example x=2) in the equation Β [tex]f(x)=0.03(2)^2\times{(2^2-25)}[/tex] , an see if the graph shows the correct value of f(x) given x, that in this case it is goint to be f(2)=-2.57.