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.

Short answer

horizontal; right

Step-by-step solution

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.