Question

How do you graph `y=-5sqrtx` and what is the domain and range?

Answer 1

To graph, derive the solution from the parent function, `f(x)=sqrt(x)`. To find the domain, eliminate the "illegal" values of `x`.
Domain is all `x>= 0`.

Explanation:

You can plug values in for `x` and determine various `y` values. However, there are a few steps that are important first.

Step 1. All graphs of square root functions are related to the parent function `f(x)=sqrt(x)`. One way to find nice integer values is to plug in perfect squares, like `x={0, 1, 4, 9, ...}`.
graph{sqrt(x)[-1,5, -1, 3]}
Step 2. While keeping all your `x` values, multiply the recently discovered `y` values by `-5`. This will give you the following graph.
graph{-5sqrt(x)[-1, 5, -12, 1]}
Step 3. To find the domain of this function, you have to determine all the "legal" values of `x`. This is accomplished by finding the "illegal" values of `x`.

The illegal values occur whenever you plug in negative values beneath the square root and whenever you would divide by zero. You don't have any fractions or denominators so there are no divide-by-zero illegal values. However, all negative numbers are excluded. So your domain can be expressed as:

Domain is all `x>= 0`