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

$\begin{gathered} \therefore y=\frac{2-3x}{x} \\ \end{gathered}$

We can simplify and find the limit.

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

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

$y=f(x)$