Question

select the correct answer. each statement describes a transformation of the graph of ( f(x) = x ). which statement correctly describes the graph of ( g(x) ) if ( g(x) = f(x - 11) )? a. it is the graph of ( f(x) ) translated 11 units up. b. it is the graph of ( f(x) ) where the slope is increased by 11. c. it is the graph of ( f(x) ) translated 11 units to the left. d. it is the graph of ( f(x) ) translated 11 units to the right.

Explanation:

For a function $f(x)$, the transformation $f(x - h)$ represents a horizontal shift of the graph. When $h>0$, the graph shifts $h$ units to the right. Here, $g(x)=f(x-11)$ with $h=11$, so the graph of $f(x)$ shifts 11 units right.

Answer:

D. It is the graph of $f(x)$ translated 11 units to the right.