/* To-Do: change all increments to .1; re-export w/mouse as dragger setting; add more text; practice problems */ Manipulating Graphs

## Manipulating Graphs

Home > Breadcrumbs > Manipulating Graphs

### BASICS:(top)

Certain transformations of a graph can be brough about the same way independently of the function being graphed. On this page, we'll look at how graphs of y=f(x)+c, y=f(x+c), and y=af(x) differ from the graph of y=f(x).

 This demo shows what happens when we add a constant c to a given function (in this case, the function y=x²). Use the slider to change the value of c and see how the graph changes. Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now) math.brown.edu, June 13, 2008, Created with GeoGebra

As you can see, this causes vertical translation.

### ADDING A CONSTANT TO X:(top)

 This demo shows what happens when we add a constant c to x inside a given function (in this case, we look at y=(x+c)²). Use the slider to change the value of c and see how the graph changes. Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now) math.brown.edu, June 13, 2008, Created with GeoGebra

As you can see, this causes horizontal translation.

### MULTIPLYING BY A CONSTANT:(top)

 This demo shows what happens when we add multiply a function by a constant a (in this case, we look at y=ax²). Use the slider to change the value of a and see how the graph changes. Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now) math.brown.edu, June 13, 2008, Created with GeoGebra

As you can see, this causes horizontal scaling.

### DIVIDING BY A CONSTANT:(top)

 This demo shows what happens when we divide a function by a constant a (in this case, we look at y=x²/a). Use the slider to change the value of a and see how the graph changes. Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now) math.brown.edu, June 13, 2008, Created with GeoGebra

As you can see, this causes vertical scaling.

### ALL TOGETHER:(top)

 In this demo, all 4 factors are combined to manipulate the function y=a(x-b)²/d+c. Use the sliders to control each variable. Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now) math.brown.edu, June 13, 2008, Created with GeoGebra

### PRACTICE PROBLEMS:(top | answers | solutions)

Graph the following: