Answer:
[tex]g(x)=|x+2|+1[/tex]
Step-by-step explanation:
Graph of a Modulus function:
- Line y = x where x ≥ 0
- Line y = -x where x ≤ 0
- Vertex at (0, 0)
Therefore, the parent function is:
[tex]\boxed{f(x)=|x|}[/tex]
(Shown in red on the given graph).
From inspection of the given graph, the blue graph is the translated function. As the left and right parts of the translated function are parallel to the left and right parts of the parent function, the graph has not been stretched and has only be translated (shifted).
To find the translation, study the vertex of both functions. The vertex has been translated 2 units left and 1 unit up.
Translations
[tex]\textsf{For $a > 0$}:[/tex]
[tex]f(x+a) \implies f(x) \: \textsf{translated $a$ units left}[/tex]
[tex]f(x-a) \implies f(x) \: \textsf{translated $a$ units right}[/tex]
[tex]f(x)+a \implies f(x) \: \textsf{translated $a$ units up}[/tex]
[tex]f(x)-a \implies f(x) \: \textsf{translated $a$ units down}[/tex]
Therefore, the equation for the translated function is:
[tex]f(x+2)+1 \implies \boxed{ g(x)=|x+2|+1}[/tex]
