1. anonymous

|dw:1441149824377:dw|

2. anonymous

Graph it. Find the domain and the range. How do I do this?

3. anonymous

4. jdoe0001

well is just a piecewise function from x < 0, you'd graph $$x^2$$ which is a parabola from 0 up to 3 over the x-axis, you'd graph x+2 which is a line and from 3 onwards towards positive infinity, you'd graph 4, or y =4, which is a horizontal line

5. jdoe0001

it'd look something like |dw:1441150875157:dw| a quadratic, then cut-off at 0, and then a slanted line, that is x+3, then cut-off, then a horizontal line

6. jdoe0001

from the graph, you can pretty much get the domain and range

7. anonymous

@jdoe0001 and the domain and range would be all real numbers?

8. jdoe0001

well, real numbers that may not include $$\pm \infty$$

9. anonymous

what do you mean?

10. jdoe0001

that may nor may not include that is, may or may not include $$\Large \pm \infty$$

11. jdoe0001

well... look at the graph, the domain is easy to get from there look how far the graph goes to the left look how far the graph goes to the right what's the domain?

12. anonymous

It looks like the graphs, when all combined together, hit all real numbers

13. jdoe0001

welll..yes... one could say $$\Large \mathbb{R}$$ or one could also say it goes from $$-\infty$$ to $$+\infty$$

14. jdoe0001

which is true, because the domain of the functon on the left-hand-side, or $$x^2$$ its domain is $$\pm\infty$$ so going to the left, that parabola will go to $$-\infty$$

15. jdoe0001

the parabola goes to 0, it doesn't contain 0, but the next equation does, x+3 so x+3 contains 0, goes up to 3 the joints up with the other equation, "4" or y =4, horizontal line and then that horizontal line, continues to $$+\infty$$

16. jdoe0001

so as you can see, from the graph, the parabola goes to $$-\infty$$ the horizontal line goes to $$+\infty$$ thus the domain is $$\mathbb{R}$$ or $$(-\infty,+\infty$$

17. jdoe0001

well, $$(-\infty,+\infty)$$ parentheses on both ends, since infinity is not a number, thus never reached

18. anonymous

thanks!

19. jdoe0001

do the same to get the domain, do the graph, and check how far up the y-axis the parabola goes, how far down, and the others

20. anonymous

Would you mind helping me with another problem?

21. jdoe0001

sure, post anew.. more eyes :)