Question

The graphs of two rational functions f and g are shown. One of them is given by the expression 2-3x/x. Which graph is it? Explain how you know.

Answer 1

Let the given function be y

`\begin{gathered} \therefore y=(2-3x)/(x) \\ \end{gathered}`

We can simplify and find the limit.

`\begin{gathered} y=(2-3x)/(x) \\ y=(2)/(x)-3 \\ As\text{ x tends to }\propto \\ \lim _(x\to\infty)((2)/(x)-3)=-3 \end{gathered}`

This means that the end behaviour of the graph would be the function tending to -3.

Looking at the two graphs, the graph with this end behaviour is

Answer

`y=f(x)`