Let's start by drawing the graph of the parent function, f(x)= 1x. The graph of this function is a hyperbola, which consists of two symmetrical parts called branches. The domain and range are all nonzero real numbers. The graph of this function has two asymptotes, the vertical line x=0 and the horizontal line y=0.
Let's now consider the function we are asked to graph.
g(x)=- 9/x
This is a rational function of the form g(x)= ax, which means it will have the same asymptotes, domain, and range as f(x)= 1x. With this in mind, let's make a table of values to find some points that lie on the graph. Make sure to include both positive and negative values for x.
x
- 9/x
g(x)=- 9/x
- 9
- 9/- 9
1
- 3
- 9/- 3
3
- 1
- 9/- 1
9
1
- 9/1
- 9
3
- 9/3
- 3
9
- 9/9
- 1
Let's plot the obtained points and connect them with a smooth curve. Keep in mind that this graph will also have two branches. Furthermore, be aware that the x- and y-axes will be the asymptotes.
We can see that the graph of g lies farther from the axes and is reflected over the x-axis. Moreover, as we have already said, the graphs have the same asymptotes, domain, and range.
