Question

The graph of f(x)=-vx is shifted to the right five units.
What is the domain?

Answer 1

Answer:

All x-values larger than or equal to 5 ($x\geq 5$)

Step-by-step explanation:

Notice that the graph of

$f(x)=-\sqrt{x}$

is defined for all real x-values larger than or equal to zero, since the square root is defined only for such values.

When we shift the graph to the right 5 units, the function becomes:

$f(x)=-\sqrt{x-5}$

then the radicand x-5 must be larger than or equal to 0 in order to render real values. Then we have:

$x-5\geq 0\\x\geq 5$

which means that now the Domain becomes the following set (in set builder notation):

$Domain=\left \{ x\,|\,x\geq 5 \right \}$