College Algebra & Trigonometry, 2018a

4.4. TRANSFORMATIONS 203
Horizontal Shifts
A function may also be shifted horizontally by adding or subtracting a number
inside the parentheses.
If we start with our original function f(x):
8
6
4
2
−8 −6 −4 −2
−2
2 4 6 8
−4
−6
−8
Then the transformation f(x − 2) will shift the graph horizontally, except that it
will move in the opposite direction of the sign. The f(x − 2) shift will move the
graph 2 places to the right whereas a shift of f(x+2)will move the graph 2 places
to the left.
The reason why this happens will be more clear if we look at a table of values for
the function:
x
f(x)
−6 0
−3 6
1 6
3 4
8 4