You can manipulate the values of the transformations and see how they affect the graph of 
.
Use the sliders to adjust the Horizontal and/or Vertical shift values, or the Horizontal and/or Vertical stretch/shrink values, or both, or enter values in the boxes.
Check the boxes to see functions reflected in the coordinate axes. You may choose a reflection in the x-axis or the y-axis, a reflection in both axes, or no reflection.
Please enter decimal numbers instead of fractions.
Exploration 1:
Reset all parameters to their initial values, and check the box for a reflection in the x-axis.
Remember what the reflected image looks like, then un-check the box. Next, check the box for a reflection in the y-axis. Compare the reflection to the previous reflection.
How do the images compare?
What is the reason for what you see?
Try using both reflections. How do you explain what you see?
Exploration 2:
Reset all parameters to their initial values. Set the horizontal stretch/shrink value to 0.5.
Memorize the graph, then reset the value to 1. Next, set the vertical stretch/shrink value to 2. Compare the result to the previous graph.
How do the graphs compare?
What is the reason for what you see?
Try using 2 for the horizontal stretch/shrink value and 0.5 for the vertical stretch/shrink value.
Do you expect similar results?
There other pairs of numbers that produce the same effect. How could they be described?
which is subject to the same stretches, shrinks and shifts as the graphs of other functions. The graph of 
