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

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PaxPolaris
  • PaxPolaris
\[\Large x \in \mathbb{R};\ \ f(x) > 2\]
anonymous
  • anonymous
Rohangrr,,you are awesome! Thank you so much for explaining this to me. I appreciate it. :)

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