## anonymous 3 years ago Determine the intervals on which f(x) is continuous. f(x) = sqrt( x + 3)

1. anonymous

@Reaper534

2. anonymous

so should i just plug in the number like 6 then add it with 3 and take the square root of the answer?

3. anonymous

@zepdrix can u help?? me

4. anonymous

@blondie16 can u help?

5. zepdrix

Are you familiar with the graph of $$y=\sqrt x$$? It's a good one to memorize, the basic shape.

6. anonymous

yes

7. zepdrix

|dw:1359680242637:dw|So this is what $$y=\sqrt x$$ looks like, yes? Our function that they gave us has a +3 under the square root. That represents a horizontal shift to the left 3 units.

8. anonymous

okay

9. zepdrix

|dw:1359680353027:dw|So our function would look like this, shifted over to the left 3 units.

10. zepdrix

I guess we actually don't need the graph to figure this one out... Let's just think about what values we're allowed to plug into a square root.

11. anonymous

okay

12. zepdrix

If you plug in x=-3, $$\large f(-3)=\sqrt{-3+3}$$ which equals $$0$$ yes? So -3 is fine. Let's try plugging in -4, $$\large f(-4)=\sqrt{-4+3}$$ which equals $$\sqrt{-1}$$. Uh oh! We can't take the square root of a negative value! :O Remember that from math rules?

13. anonymous

yes i do

14. zepdrix

When you need to determine intervals of continuity, you just need to look for numbers that would cause a problem. Those are places where your function is not continuous. So we would NOT include those values in our interval.

15. anonymous

okay

16. zepdrix

It turns out that you can plug in larger and larger values of x in the positive direction and you'll get real solutions for f(x). That just means, none of the positive x values are a problem. It seems that if $$x \lt -3$$, it creates a negative value under the square root, which is a problem.

17. zepdrix

So our interval would start from -3 and go up to positive infinity, those are all of the x values we can use.

18. zepdrix

In interval notation we would write it like this,$\huge [-3,\infty)$ See the square bracket? That's to show that we want to include the value -3. If we had done a rounded bracket around the -3, it would mean we start at -3 but don't include the number itself. And also, we always put a rounded bracket on infinity. It's not an actual number so we can't include it.

19. anonymous

okay

20. anonymous

okay got you