Finding the Range of the Function f(x)=x²+4: Interval Notation Explanation

[credico]

Find the range of the equation.
f(x)=x²+4Things I know for sure:
x²>=0

We are brushing up on functions and interval notation in my calc class, and I can't remember how to do this in interval notation. If x is a number being squared it has to be positive or zero. So at the minimum the answer is going to be:
f(x)=0+3

f(x)=3

So the interval notation would be what? Quick little explanation would help as well. Thanks.

 

[Office_Shredder]

The domain of the function is all the possible inputs for your function. You seem to be looking at the range

 

[credico]

You're right, that's what I meant. Good call. But what about interval notation?

 

[Feldoh]

Careful, I think you're confusing domain and range.

The range is [4,inf), the domain is (-inf,inf).

Basically the domain is a set of numbers that x can satisfy. For example g(x) = 1/x the domain is (-inf,0)U(0,inf) because g(x) is not defined at x=0.

The range is a set of numbers that your function can have as a value for a given domain of values. For example h(x) = x^2 has a range of [0,inf) since the minimum value of h(x) is 0 and the function will extend to infinity.

If a number is exclusive we use parenthesis, and if a number is inclusive we use brackets. So in the case of the domain of g(x) = 1/x, x cannot equal zero but it can approach the value of 0 so 0 is exclusive. Negative and positive infinity are always exclusive since they are not actual values. Therefore (-inf,0) is in parenthesis on both sides. But that's not the entire domain! We can have x>0 so we need to include that too. We write include (or union) with a capitol U so the answer is (-inf,0)U(0,inf).

 

[credico]

Great, that helps a lot. Thanks.