Can someone explain to me what domain and range is and how i would find it for this function? (attached)
Stacey Warren - Expert brainly.com
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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.