Explanation
Given a function f(x) we translate the function:
• a units horizontally (a > 0 to the right, a < 0 to the left),
,
• b units vertically (b > 0 up, b < 0 down),
by the transformation:
[tex]f(x)\rightarrow g(x)=f(x-a)+b.[/tex]
In this case, we have:
[tex]\begin{gathered} f(x)=|x|, \\ g(x)=|x-2|+4=f(x-2)+4. \end{gathered}[/tex]
Comparing f(x) and g(x) with the general transformation above, we see that the graph of g(x) is the graph of f(x) translated:
• a = 2 units to the right,
,
• b = 4 units up.
Translating the graph of f(x), we get:
Answer
The translated graph is the graph in red:
