Finding the range of an equation with domain restrictions?

[Cheesycheese213]

I got a bit confused on how I'm supposed to do restrictions on an equation?

I had an equation (eg. y = 2^x), and I wanted to get the domain and range. I had said the domain was that {x ∈ N} (natural numbers), since it was a sequence, but I got a bit confused on how I was supposed to do the range?

If I just do it from the equation itself, I get {y ∈ R | y > 0}, since the powers of positive numbers can only be positive. But if I also included {x ∈ N}, I'd get that {y ∈ R | y ≥ 2}, since the smallest x value possible is 1, and 2¹ = 2?

Am I supposed to base the range off of the equation only, or the domain of the x as well? Thanks!

 

[Mark44]

I got a bit confused on how I'm supposed to do restrictions on an equation?

I had an equation (eg. y = 2^x), and I wanted to get the domain and range. I had said the domain was that {x ∈ N} (natural numbers), since it was a sequence, but I got a bit confused on how I was supposed to do the range?

If I just do it from the equation itself, I get {y ∈ R | y > 0}, since the powers of positive numbers can only be positive. But if I also included {x ∈ N}, I'd get that {y ∈ R | y ≥ 2}, since the smallest x value possible is 1, and 2¹ = 2?

Am I supposed to base the range off of the equation only, or the domain of the x as well? Thanks!

Well, the range will depend on the domain. If there aren't any restrictions on the domain, i.e., $x \in \mathbb R$, then the range will be as you said -- all positive real numbers.
However, if the inputs are in a sequence (which you said, but didn't elaborate on) or if the inputs are the positive integers, then the range will also be a sequence of numbers.

For example, if $x \in \mathbb N$, then $y \in \{2, 4, \dots, 2^n, \dots \}$

 

[Cheesycheese213]

Well, the range will depend on the domain. If there aren't any restrictions on the domain, i.e., $x \in \mathbb R$, then the range will be as you said -- all positive real numbers.
However, if the inputs are in a sequence (which you said, but didn't elaborate on) or if the inputs are the positive integers, then the range will also be a sequence of numbers.

For example, if $x \in \mathbb N$, then $y \in \{2, 4, \dots, 2^n, \dots \}$

Oooh I see thank you so much!