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)=0.1/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
0.1/x
g(x)=0.1/x
- 1
0.1/- 1
- 0.1
- 0.5
0.1/- 0.5
- 0.2
- 0.2
0.1/- 0.2
- 0.5
- 0.1
0.1/- 0.1
- 1
0.1
0.1/0.1
1
0.2
0.1/0.2
0.5
0.5
0.1/0.5
0.2
1
0.1/1
0.1
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 closer from the axes than the graph of f. Moreover, both graphs lie in the first and third quadrants. Finally, as we have already said, the graphs have the same asymptotes, domain, and range.
