Precalculus with Limits: A Graphing Approach, Sixth Edition
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Precalculus with Limits: A Graphing Approach, Sixth Edition View details
4. Shifting, Reflecting, and Stretching Graphs
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Exercise 1 Page 47

We want to name three types of rigid transformations. First, recall that rigid transformations can only change the position of the graph of a function in the coordinate plane. The basic shape of the graph remains unchanged. Horizontal shifts, vertical shifts, and reflections are examples to this type of transformations.
Rigid Transformations of the Graph of f(x)
Vertical Shifts Vertical shift k units upward, k>0

y=f(x)+k

Vertical shift k units downward, k>0

y=f(x)-k

Horizontal Shifts Horizontal shift h units to the right, h>0

y=f(x-h)

Horizontal shift h units to the left, h>0

y=f(x+h)

Reflections Reflection in the x-axis
y=- f(x)
Reflection in the y-axis
y=f(- x)