How many vertical asymptotes does the graph of this function have? f(x)=5/3x(x+1)(x-7)

The graph of the function has three vertical  asymptotes

Step-by-step explanation:

we have the function

we know that

To find the vertical asymptotes of a rational function, simply set the denominator equal to 0 and solve for x.

so

The values of x are x=-1,x=0, x=7

using a graphing tool

see the attached figure to better understand the problem

therefore

The graph of the function has three vertical asymptotes

the answers c