Q. 1 - Precalculus Enhanced with Graphing Utilities

Question

Suppose that the graph of a function f is known. Then the graph of $y=f(x-2)$ may be obtained by a(n) ________ shift of the graph of $f$ to the ________ a distance of $2$ units. 

Step-by-Step Solution

Answer

horizontal; right

Step 1. Concept Used

If the argument $x$ of a function $f$ is replaced by $x-h$, $h>0$, the graph of the new function $y=f(x-h)$ is the graph of $f$ shifted horizontally right $h$ units.

If the argument $x$ of a function $f$ is replaced by $x+h$, $h>0$, the graph of the new function $y=f(x+h)$ is the graph of $f$ shifted horizontally left $h$ units. 

Step 2. Fill in the blanks

When the argument $x$ of a function $f$ is replaced by $x-2$, then the new function $y=f(x-2)$ is the graph of $f$ shifted horizontally right $2$ units.

So if the graph of a function $f$ is known. Then the graph of $y=f(x-2)$ may be obtained by a horizontal shift of the graph of $f$ to the right a distance of $2$ units.