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Transformations

When a function gets either compressed, shifted, or even stretched to become a
whole new function
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Vertical Shifts
y=f(x)+k

Raising the graph of f by k units by adding k to f (x)
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y=f(x)-k

Lowering the graph of f by k units by subtracting k to f (x)
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Horizontal Shifts
y=f(x+h)

Shifting the graph of f to the left by h units by replacing x by x + h
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y=f(x-h)

Shifting the graph of f to the right by h units by replacing x by x − h
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Compressing
y=af(x)

First by multiplying every y-coordinate of y = f (x) by a, second by stretching
the graph of f vertically if and when a > 1, and finally by compressing the
graph of f vertically if 0 < a < 1
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Stretching
y=f(ax)

First by replacing x with ax, second by multiplying every x-coordinate of y =
1
f (x) by x , third by stretching the graph of f vertically if and when 0 < a < 1,
and finally by compressing the graph of f vertically if a > 1
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Reflection
About the X-Axis

Reflecting the graph of f about the x-axis by multiplying f (x) by −1 to make
it the following:
y = −f (x)

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