## sh3lsh 4 years ago 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?

1. Mertsj

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

2. 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

3. sh3lsh

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

4. Mertsj

Well is the 2 positive or negative?

5. sh3lsh

positive :|

6. Mertsj

Is the seven positive or negative?

7. sh3lsh

The equation is just like how i typed it.

8. Mertsj

9. sh3lsh

positive.

10. Mertsj

Is the seven positive or negative?

11. Mertsj

Is the square root of x positive or negative?

12. sh3lsh

positive

13. Mertsj

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

14. Mertsj

|dw:1326851598024:dw|

15. Mertsj

y = positive over positive plus positive.

16. Mertsj

Will y always be positive?

17. sh3lsh

yes?

18. Mertsj

So the range must be all real numbers greater than 0

19. 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

20. sh3lsh

okay . I'll be practicing. Thanks.