Transformation of Graphs 图的变换

This applet shows you the effect of each transformation on a graph.

Mobile Phones and iPads do not support Java. Please run Java Applets on your laptops or desktops.
Edge and Google Chrome do not support Java. Please use Internet Explorer, Firefox or Safari.
If the applet does not appear, please try the following:
(1) Download the Java software from www.java.com.
(2) Go to the menu: Tools > Turn off Pop-Up Blocker.
(3) Tools > Internet Options > Advanced > Security > Allow Active Contents.
(4) Start Menu > All Programs > Java > Configure Java > Security and then add this website to the Exception Site List.
Exercises for students
Sketch the following curves on paper and check your graphs using the above applet:
y = 2 sin(x),y = 0.5 sin(x),y = sin(2x),y = sin(0.5x), y = sin(x - 1),y = sin(x + 1)
y = sin(x) + 1,y = sin(x) - 1,y = (x+1)2,y = (x-1)2,y = x2 + 1,y = x2 - 1
y = 1/x,y = 1/(x-1),y = exp(x-1),y = exp(x) - 1


Summary
y = a f(x)The graph is scaled by factor a parallel to the y-axis.
If a is negative, the graph is reflected in the x-axis.
y = f(ax)The graph is scaled by factor 1/a parallel to the x-axis.
If a is negative, the graph is reflected in the y-axis.
y = f(x + a)The graph is translated in the direction of the negative x-axis by a units.
If a is negative, the graph is translated in the direction of the positive x-axis.
y = f(x) + aThe graph is translated in the direction of the positive y-axis by a units.
If a is negative, the graph is translated in the direction of the negative y-axis.








Right-click here to download this page and the Java Class File.

Back to H2 Mathematics Homepage