Vertical graph transformations
- Author:
- matheagle
- Topic:
- Algebra, Function Graph
Instructions for initial exploration
The graph of is shown in red. The function probably doesn't have such a nice notation/formula, but this red picture with several bends will be helpful for illustrating what is happening with graph transformations. By default we start with and though you may change these (and to reset, just reload the webpage). The graph of is shown in blue. With the default values, the blue graph occupies the same space as the red graph.
First, draw a picture of the red graph on paper, carefully labeling the x and y coordinates of the 5 special points, and writing the caption near this picture.
Then, change from 1 to 2. On a new set of axes, draw a picture of the blue graph on paper, carefully labeling the 5 special points, and writing the caption near this picture. Use your own words to describe what happened: how would you get from the picture to the picture?
Finally, while keeping change the value of from 0 to 1. On a new set of axes, draw a picture of the new blue graph on paper, carefully labeling the 5 special points, and writing the caption near this picture. Use your own words to describe what happened: how would you get from the picture to the picture?
To test your understanding, what do you think does in general, and what do you think does in general? Verify your conjectures by graphing in stages on paper first, and reload this app, using this app to check (first changing c, then changing d). Then, challenge yourself by writing your own question: reload the app, and be sure to always set the "c" value first, then set the "d" value next. (If you need to, you can zoom in and out by scrolling or using a mouse scroll wheel inside the graphing pane.)