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

Identify the vertical asymptotes, horizontal asymtope, domain, range. Sketch the graph-example-1

1 Answer

6 votes

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.

Identify the vertical asymptotes, horizontal asymtope, domain, range. Sketch the graph-example-1
User Gonczor
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