Question

Identify the vertical asymptotes, horizontal asymtope, domain, range. Sketch the graph

Answer 1

The given function is,

`f(x)=-(4)/(x-2)+1`

The domain can be determined as,

`\begin{gathered} x-2\\e0 \\ x\\e2 \\ x\in R-\lbrace2\rbrace \end{gathered}`

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,

`y\in\in R-\lbrace1\rbrace`

Thus, the required range of the function is set of all real numbers excluding 1.