Manipulating Graphs
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Graph Manip.: Basics :: Adding a Constant :: Adding a Constant to x :: Multiplying by a Constant :: Dividing by a Constant :: All Together :: Practice Problems :: Quiz
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).
ADDING A CONSTANT: (top)
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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.
math.brown.edu, June 13, 2008, Created with GeoGebra |
As you can see, this causes vertical translation.
ADDING A CONSTANT TO X: (top)
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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.
math.brown.edu, June 13, 2008, Created with GeoGebra |
As you can see, this causes horizontal translation.
MULTIPLYING BY A CONSTANT: (top)
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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.
math.brown.edu, June 13, 2008, Created with GeoGebra |
As you can see, this causes horizontal scaling.
DIVIDING BY A CONSTANT: (top)
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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.
math.brown.edu, June 13, 2008, Created with GeoGebra |
As you can see, this causes vertical scaling.
ALL TOGETHER: (top)
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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.
math.brown.edu, June 13, 2008, Created with GeoGebra |
PRACTICE PROBLEMS: (top | answers | solutions)
Graph the following:
- (answer | solution)
- (answer | solution)
- (answer | solution)
This page last updated 1 August, 2008 9:38 PM