Question

Given the graph of function f. Identify the function by name. Then graph the indicated functions: 2 f(x) & 1/2 f(x)A) state the domain and range of each Use set notation.

Answer 1

Okay, here we have this:

From the graph we can see that it is the square root function, that is, we have the following function:

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

Nowm according with this let's graph 2 f(x) and 1/2 f(x) and let's determine the domain and range of each one::

2f(x):

$2f(x)=2\cdot\sqrt[]{x}$

1/2f(x):

$\frac{1}{2}f(x)=\frac{1}{2}\sqrt[]{x}$

If we graph these functions we obtain the following:

Now, from the graphs of the functions we obtain that the domain and range of these are the same:

Domain: [x | x≥0]

Range: [f(x) | f(x)≥0]