THe red line is f(x) + 2, the blue line is f(x) - 2. When you add to a function, the function shifts up, when you rest it shifts down
The domain and range of the square root is D = [0, infinity) R = [0, infinity)
The domain and range of f(x) + 2 is D = [0, infinity) R = [2, infinity)
The domain and range of f(x) - 2 is D = [0, infinity) R = [-2, infinity)
Domain and range square root = f(x):
[tex]\begin{gathered} D=\lbrack x\colon x\ge0\rbrack \\ R=\lbrack y\colon y\ge0\rbrack \end{gathered}[/tex]
Domain and range f(x) + 2:
[tex]\begin{gathered} D=\lbrack x\colon x\ge0\rbrack \\ R=\lbrack y\colon y\ge2\rbrack \end{gathered}[/tex]
Domain and range f(x) - 2:
[tex]\begin{gathered} D=\lbrack x\colon x\ge0\rbrack \\ R=\lbrack y\colon y\ge-2\rbrack \end{gathered}[/tex]
