Question

Can someone explain to me what domain and range is and how i would find it for this function? (attached)

Answer 1

Don't think of it as domain and range; think of it as x and y. The domain is x and the range is y. If you were to try to graph this, are there any values of x and y that would be outlawed?

For example, if f(x) = 1/x, then x cannot be 0, because 1/0 is undefined. Similarly, if f(x) = 1/(x + 2), then x cannot be -2, because 1/(-2 + 2) = 1/0, and again, undefined.

So, in your example, what can x not be?

And the answer is, x can be any real number. If x > 0, the function works. If x < 0, the function works, and if x = 0 the function works. So the domain is all real numbers.

The range on the other hand....

Let's pay attention to (1/2)^x

When x = 0, this = 1
When x > 1, this gets smaller and smaller, going toward 0, but not getting there.
(1/2)^2 = 1/2
(1/2)^2 = 1/4
(1/2)^3 = 1/8
"going toward 0, but not getting there" means this is asymptotic to y = 0, by the way.

When x < 0, we're taking inverses

(1/2)^-1 = 2^1 = 2
(1/2)^-2 = 2^2 = 4
(1/2)^-3 = 2^3 = 8
And by the way, the function is asymptotic to x = 0

So the range of g(x) = (1/2)^x is always going to be positive, that is g(x) > 0

But we're dealing with f(x) = (1/2)^2 - 3

So f(x) > -3

And that's the range.

Answer 2

thanx

Answer 3

\[\Large x \in \mathbb{R};\ \ f(x) > 2\]

Answer 4

Rohangrr,,you are awesome! Thank you so much for explaining this to me. I appreciate it. :)