Sketching graphs looks hard but if you follow the rules carefully they can be very easy.
| Ways of Transforming
Translating, stretching, squashing and reflecting | y = f(x) + a
f(x) is the equation that was used to draw the graph
f(x) + a says "add (or subtract) the value a from the value of y"
This will result in the graph being moved up (or down) the y axis
| y = f(x + a)
f(x) is the equation that was used to draw the graph
f(x + a) says "add (or subtract) the value a from the value of x"
This will result in the graph being moved left (or right) along the x axis
Note : adding a value moves the graph LEFT i.e. more negative x | y = af(x)
f(x) is the equation that was used to draw the graph
af(x) says "multiply y by the value a"
This will result in the graph being reflected, stretched or squashed, vertically
If a is negative the graph will be reflected in the x axis
If a is > 1 (or < -1) it will be stretched vertically
If a is < 1 and > -1 (-1 < a < 1) it will be squashed, vertically
| y = f(ax)
f(x) is the equation that was used to draw the graph
f(ax) says "multiply x by the value a"
This will result in the graph being reflected, stretched or squeezed, horizontally
If a is negative the graph will be reflected in the y axis
If a is > 1 (or < -1) it will be squashed horizontally
If a is < 1 and > -1 (-1 < a < 1) it will be stretched horizontally
Note : Squashing and Stretching are the reverse of the vertical equation | I am not yet very sure about reflecting, stretching and squashing
especially when the numbers are complicated
I need to do a lot more work on this one !! |
| notes
A "normal" is another name for a perpendicular line from a tangent.
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