First, when the graph of is changed into , all the -values are multiplied by . In other words, the graph is stretched up and down by a factor of , from the -axis. Instead of taking values from to , therefore, it will take values from to .
Next, when is changed into , all the -values have their sign changed. In other words, the graph is reflected in the -axis. So, for example, when instead of .
Finally, changing into adds to all the -values. In other words, the graph is shifted (translated) upwards by units.
- Can you sketch the graph for #1 now?
- Can you do #2 in the same way?
I assume that for #3 you mean
Clearly, this is related to the graph of
which you can sketch using the same techniques as above. Then, you need to learn that when is changed into , the graph is translated units to the left.
Yes, it is to the left, not the right, because when , the value of is . So the new graph starts at the point where on the original graph. So it is exactly the same as the original, but it's units to the left. (You may need to think a bit about that!)
Can you complete #3 now?