Mathematics
OpenStudy (sh3lsh):

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?

OpenStudy (mertsj):

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

OpenStudy (mertsj):

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

OpenStudy (sh3lsh):

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

OpenStudy (mertsj):

Well is the 2 positive or negative?

OpenStudy (sh3lsh):

positive :|

OpenStudy (mertsj):

Is the seven positive or negative?

OpenStudy (sh3lsh):

The equation is just like how i typed it.

OpenStudy (mertsj):

OpenStudy (sh3lsh):

positive.

OpenStudy (mertsj):

Is the seven positive or negative?

OpenStudy (mertsj):

Is the square root of x positive or negative?

OpenStudy (sh3lsh):

positive

OpenStudy (mertsj):

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

OpenStudy (mertsj):

|dw:1326851598024:dw|

OpenStudy (mertsj):

y = positive over positive plus positive.

OpenStudy (mertsj):

Will y always be positive?

OpenStudy (sh3lsh):

yes?

OpenStudy (mertsj):

So the range must be all real numbers greater than 0

OpenStudy (mertsj):

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

OpenStudy (sh3lsh):

okay . I'll be practicing. Thanks.