The given function is,
[tex]f(x)=-\frac{4}{x-2}+1[/tex]
The domain can be determined as,
[tex]\begin{gathered} x-2\ne0 \\ x\ne2 \\ x\in R-\lbrace2\rbrace \end{gathered}[/tex]
Thus, the domain is the set of real numbers excluding the number 2.
The graph can be drawn as,
The vertical asymtotes is x=2 as the fuction attains the value of infinty and negative infinity at x=2.
The horizontal asymtotes is y=1 as at this value of function the value of x is either infinity or negative of infinity.
The range of the function is,
[tex]y\in\in R-\lbrace1\rbrace[/tex]
Thus, the required range of the function is set of all real numbers excluding 1.
