Question

How do you find the domain of `y = sqrt(4-2x)`?

Answer 1

`(-oo,2]`

Explanation:

In any square root function, the "argument" of the square root, or the thing inside the square root function, must be greater than `0`.

Thus, the domain can be found through finding the "switching point," or the point where the term inside the square root function switches from positive to negative. This will occur when the term is `0`.

`4-2x=0`
`4=2x`
`x=2`

The square root is `0` when `x=2`. Now, figure out when the term will be positive. This will be the domain.

When `x<2`:

`4-2(0)=4`

It is positive. We can check when `x>2`:

`4-2(3)=-2`

This is negative, so this won't work.

Thus, the domain of the function is `(-oo,2]`, since all the values `2` and less do work.

(This domain can also be written as `x<=2`.)

graph{sqrt(4-2x) [-14.77, 13.71, -4.27, 9.97]}