Question

Given the graph of a function f. A) identify the function by name B) then graph the indicated functions : f(x) + 2 ; f(x) - 2C) state the domain and range of each.Use set notation.

Answer 1

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):

`\begin{gathered} D=\lbrack x\colon x\ge0\rbrack \\ R=\lbrack y\colon y\ge0\rbrack \end{gathered}`

Domain and range f(x) + 2:

`\begin{gathered} D=\lbrack x\colon x\ge0\rbrack \\ R=\lbrack y\colon y\ge2\rbrack \end{gathered}`

Domain and range f(x) - 2:

`\begin{gathered} D=\lbrack x\colon x\ge0\rbrack \\ R=\lbrack y\colon y\ge-2\rbrack \end{gathered}`