Question

How do you find the domain and range for `y= -2x+3, x>0`?

Answer 1

Domain: `(0, +oo)`
Range: `(-oo, 3)`

Explanation:

The problem actually gives you the domain of the function as being described by `x>0`.

More specifically, the domain of the functioncannot include negative values of `x`, as well as `x=0`.

This means that the domain of the function will be `(0,+oo)`.

Now for the range of the function. SInce `x` is always positive, the term `-2x` will always be negative. You can find the range of the function by using `x=0` to find the maximum value `f(x)` cannot take

`f(0) = -2 * 0 + 3 = 3`

This means that the function's range will be `(-oo, 3)`, since `f(x)` will produce a value smaller than `3` for any `x` belonging to the `(0, +oo)` domain.