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?

Question

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?

mertsj · Answer

By inspecting the equation and garnering any information you can about the y values.

mertsj · Answer

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

sh3lsh · Answer

what about an equation like f(x)= $$(2/(7+\sqrt{x)})$$

mertsj · Answer

Well is the 2 positive or negative?

sh3lsh · Answer

positive :|

mertsj · Answer

Is the seven positive or negative?

sh3lsh · Answer

The equation is just like how i typed it.

mertsj · Answer

Answer my question if you want me to help you understand.

sh3lsh · Answer

positive.

mertsj · Answer

Is the seven positive or negative?

mertsj · Answer

Is the square root of x positive or negative?

sh3lsh · Answer

positive

mertsj · Answer

so look what we have:  I will draw a picture:

mertsj · Answer

|dw:1326851598024:dw|

mertsj · Answer

y = positive over positive plus positive.

mertsj · Answer

Will y always be positive?

sh3lsh · Answer

yes?

mertsj · Answer

So the range must be all real numbers greater than 0

mertsj · Answer

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

sh3lsh · Answer

okay . I'll be practicing. Thanks.