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

+25 = x

step-by-step explanation:

here x is the hypotenuse of a right triangle whose legs are 7 and 24.   by the pythagorean theorem, 7² + 24² must equal x²:

x² = 49 + 576 = 625.   thus, x = +√625 = +25 = x