Finding the Zeros of a Rational Function

[ghostbuster25]

I have been asked to draw the graph of the function f(x)= (x+3)/(x-2)

I have found where it cuts the y-axis by putting x=0 but am unsure of how to find the x value.
I found the inverse of f(x)= (x+3)/(x-2) which gave me x= (y+3)/(y-2) then set y=0 which again gave me x=-3

I have checked on graphing calculators and this is the correct answer but i think my method is wrong!

Could anyone please help?

 

[cyby]

Information you need to know when you're graphing rational functions include... asymptotes and roots.

Do you know where your horizontal asymptotes are? What about the vertical asymptotes? Beware, because your graphing calculator may or may not show asymptotes properly!

What about the roots of this function?

 

[eumyang]

(Assuming that the denominator is not zero,) a fraction equals zero if the numerator equals zero. So to find the zeros of the function
$$f(x) = \frac{x + 3}{x - 2}$$
set the numerator equal to zero.