How do find a range of a function without graphing it? I know when you have to find the domain you usually set the equation greater than 0 depending on the equation or just fill in numbers but what do you do for range?

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How do find a range of a function without graphing it? I know when you have to find the domain you usually set the equation greater than 0 depending on the equation or just fill in numbers but what do you do for range?

Mathematics
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By inspecting the equation and garnering any information you can about the y values.
For example if the function is y=x^2, I can tell that there will never be a negative y value because x^2 is always positive unless x is 0 in which case y is 0. So I can say that the range is all positive real numbers plus 0
what about an equation like f(x)= \[(2/(7+\sqrt{x)})\]

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Well is the 2 positive or negative?
positive :|
Is the seven positive or negative?
The equation is just like how i typed it.
Answer my question if you want me to help you understand.
positive.
Is the seven positive or negative?
Is the square root of x positive or negative?
positive
so look what we have: I will draw a picture:
|dw:1326851598024:dw|
y = positive over positive plus positive.
Will y always be positive?
yes?
So the range must be all real numbers greater than 0
Actually we could say all real numbers greater than or equal to 2/7 because the smallest thing the square root of x can be is 0 so the fraction will always be at least 2/7
okay . I'll be practicing. Thanks.

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