More Transformations of y = 1/x.
Question: What happens to the graph of y = 1/x when you add or subtract a constant to the entire equation?
This section will show what happens when you change the equation of y = 1/x to something of the form y = (1/x) +/- k, where k is some constant integer. We first need to graph the equations. Let us choose k= 5 once again. Our equations to graph will be y = 1/x, y = (1/x)+5, and y = (1/x)-5. We should always start off with the basic graph of y = 1/x.
| The Basic graph of y = 1/x |  |
Now lets take a look at what happens when we graph y = (1/x)+5.
| The graph of y = (1/x)+5 |  |
Lets look at the graph of y = (1/x) - 5
| The graph of y = (1/x)-5 |  |
Notice |
Do the graphs look any different? You should notice that the graphs shift units up and down. When the constant k is on the outside and it is added, the basic graph shifts up k units. When k is subtracted from basic graph then the basic graph is shifted down k units. |
| Notice the Asymptotes | The original asypmtotes were at x = 0 and y = 0. Notice that when the basic graph is shifted k units up or k units down that the horizontal asymptote shifts k units in the same direction. The vertical asymptote stays the same. |
LOOKING AT ALL THE GRAPHS
| Graphing the equations y = 1/x, y =(1/x)+5, and y=(1/x)-5. |  |
The graph of all three equations makes it easier to see that the vertical asymptotes do not change when shifting the graph up or down k units.