Compression and Stretch
What happens when we multiply the entire equation y = 1/x by some constant?
Let us see what happens when we multiply the equation y = 1/x by k, where k = 5.
| y = 1/x |  |
| y = 5*(1/x) |  |
| NOTICE | That the graph stretched out by a multiple of 5 units. This means that it gets smaller and bigger at a faster rate than it did before. |
Does a stretch always occur no matter what the value of k is? Lets find out!
Now lets try a fraction. Let k = 0.5 or (1/2). Lets see what the graph will look like now.
| y = 1/x |  |
| y = (0.5)*(1/x) |  |
| NOTICE | The graph has been compressed by a factor of 0.5. Basically it takes the function longer to get bigger or smaller than it did before. |
What about a negative number for k?
Let us now try to see if a stretch or a compression will occur when k is negative. Let us make k = -5 for y = k*(1/x).
| y = 1/x | |
| y = (-5)*(1/x) |  |
| NOTICE | Notice that the graph has changed. The graph as reflected itself about the x axis. |
Keep In Mind
Values for k for y = k*(1/x) |
Result |
| k > 1 |
Vertical stretch |
0 < k < 1 |
Vertical Compression |
k < 0 |
Reflection about the x axis |