In this interactive, you can play around with constants to transform functions and their graphs.
In particular, for base function f, the interactive will show the graph of y=a*f(bx+c)+d.
Base Function:
a:
b:
c:
d:
Graph of:
Show Grid
Show Axes
Label Axes
Draw Points
Label Points
Show Original Graph
Show Graph of y= for comparison
Draw Guidelines
Color Indicators (experimental)
Graph resolution:
Suggestions for Use
Play around with the various constants to try to get a sense of what they do. Be sure to change the base function to make sure your hypotheses hold for other base functions as well.
Be sure to check your hypotheses with the semicircle (sqrt(1-x^2)) or trigonometric (sin(x) or cos(x)) functions.
Try adjusting the second and third constants (inside the parentheses) at the same time. Does the graph stretch before shifting or after? Hint: it may help to check the "draw guidelines" checkbox.
Try adjusting all of the constants, and checking "draw key points" and "label key points". Verify that the moved key point falls on the graph, by plugging it into the equation. What number did you wind up having to plug into the base function?
Check "show original graph" and try to find different constants that give you the same graph, or nearly the same graph. Try this for various base functions. Once you find one, try simplifying the equation for the new graph.
Play around with the case where the base function is x. How does this relate to what we learned when studying lines?
Try reducing the graph resolution. See if you can figure out how this function grapher works.
Stretch a Cat
The cat below consists of a series of points connected by lines. The x and y coordinates of these points are multiplied by the constants you specify.
How are stretching, squashing, and mirroring related?
Horizontal:
Vertical:
Guessing Game
The interactive below will give you the graph of a function and ask you to guess a formula for the graph.
You'll be able to compare your guess with the goal
Note that there may be many solutions.