You can manipulate the values of the transformations and see how they affect the parent graph.
Click on the buttons numbered 1 to 6 to select the parent function.
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:
Try applying both reflections, separately and together, to each of the parent functions.
Can the graph of a function appear to be unchanged after a reflection in the y-axis?
After a reflection in the x-axis?
After a reflection in both axes?
Exploration 2:
Experiment with applying reflections before and after other types of transformations.
Is there a difference in the graph of a function if a reflection is applied before a stretch or shrink as opposed to after?
Jane applies a reflection in the y-axis, then a horizontal shift two units to the right, to the graph of a function. Jack applies the horizontal shift two units to the right, then the reflection in the y-axis, to the graph of the same function. Do their graphs look the same, or different?
Mark applies a reflection in the y-axis, then a vertical shift five units up, to the graph of a function. Mary applies the vertical shift five units up, then the reflection in the y-axis, to the graph of the same function. Do their graphs look the same, or different?
Exploration 3:
A shift may be combined with a stretch/shrink without a reflection.
Is a shift 4 units to the left followed by a horizontal compression by a half the same as a horizontal compression by a half followed by a shift 4 units to the left?
Is a shift 4 units to the left followed by a vertical compression by a half the same as a vertical compression by a half followed by a shift 4 units to the left?
