Horizontal Transformation: Sliding a Function Sideways
Horizontal Transformation: Sliding a Function Sideways
Question
This is the graph of :
Sketch the graph of .
Solution
The change from to
is called a horizontal transformation; it slides the function sideways. The graph of
lies one unit to the right of the graph of
. This may be counterintuitive, so let’s look at some numbers. At each x-value, the graph of
takes the y-value that the graph of
takes one unit earlier. Some values on the two graphs look like this:
The y-values from the original graph have all chugged along to correspond to higher x-values than they did before.
At any x-value on the graph, the function operates on the value 1 unit to the left of that x-value. That has the effect of moving the curve 1 unit to the right.
Similarly, graphs one unit to the left of
. Note that this is different from
which graphs one unit up from
because the 1 that gets added to the function means 1 gets added to every y-value. Similarly,
graphs one unit below
If you don’t believe me on any of these, try playing around with values of a simple function to see what happens.