Consider the function
f(x) = ![\frac{x-3}{x-4}](https://tex.z-dn.net/?f=%5Cfrac%7Bx-3%7D%7Bx-4%7D)
Domain of the function = All real numbers except , x≠4 .
![y=\frac{x-3}{x-4} \\\\ xy - 4y = x-3 \\\\ x y -x= 4 y-3\\\\ x=\frac{4 y-3}{y-1}](https://tex.z-dn.net/?f=y%3D%5Cfrac%7Bx-3%7D%7Bx-4%7D%20%5C%5C%5C%5C%20xy%20-%204y%20%3D%20x-3%20%5C%5C%5C%5C%20x%20y%20-x%3D%204%20y-3%5C%5C%5C%5C%20x%3D%5Cfrac%7B4%20y-3%7D%7By-1%7D)
Range = All real numbers except , y≠1 .
Horizontal Asymptote= Since the degree of numerator and denominator of rational function is same , So Divide coefficient of x in numerator by divide coefficient of x in denominator.
So Horizontal Asymptote , is : y=1
To get vertical asymptote, put
Denominator =0
x-4=0
x=4 , is vertical asymptote.
Domain = All real numbers except vertical Asymptote
Range = All real numbers except Horizontal Asymptote