Step-by-step explanation:
So let classify each function.
38 is a quadratic because it has a leading variable raised to the 2nd degree.
Quadratics always accept all x values positive or negative so the domain
- All Real Numbers, (- ♾,♾)
Quadratics lowest range is it vertex. The vertex of a typically quadratic is 0 because when we have the function
[tex] {x}^{2} [/tex]
we have no value after it so 0 is the lowest number.
However we have
[tex] {x}^{2} - 9[/tex]
So this means that our lowest value will be -9.
We include that point as well. The leading coeffceint is positive so it approach infinity so the range is
39 is a square root function because it has the square root symbol. Remeber that we can't take the square root of a negative number i.e( we can but it isn't graphable on a Cartesian plane). So this means x has to be greater than or equal to zero. We can take the square root of 0.
So set the equation inside the radical equal to zero.
[tex]x - 4 = 0[/tex]
[tex]x = 4[/tex]
So this means the domain is
In a square root function, we restrict our domain to only positive number so the range is
[0,♾)
