Question

Find the domain and range of the functions below

Answer 1

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

`{x}^(2)`

we have no value after it so 0 is the lowest number.

However we have

`{x}^(2) - 9`

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

• [-9,♾),

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.

`x - 4 = 0`

`x = 4`

So this means the domain is

• [4,♾)

In a square root function, we restrict our domain to only positive number so the range is

[0,♾)