Question

Given the graph of a function f. Identify the function by name. Then graph the indicated functions: -f(x) and f(x+2) -4State the domain and range of each. Use set notation.

Answer 1

The given function is

`f(x)=\sqrt[]{x}`

then -f(x) is

`h(x)=-\sqrt[]{x}`

and f(x+2)-4 is

`g(x)=\sqrt[]{x+2}-4`

Now, lets make the graph of -f(x) and f(x+2)-4:

Graph A is in purple color and graph B is in black color. The original function is in green color.

The domain of the parent function f(x) is

`\begin{gathered} x\in\lbrack0,\infty) \\ or\text{ equivalently} \\ x\in\mathfrak{\Re ^+} \end{gathered}`

and the range is

`\begin{gathered} y\in\lbrack0,\infty) \\ or\text{ equivalently} \\ y\in\mathfrak{\Re ^+} \end{gathered}`

For the purple curve, the domain is

`x\in\lbrack0,\infty)`

and the range is

`y\le0`

For the black curve, the domain is

`x\ge-2`

and the range is

`y\ge-4`