## mathmath333 one year ago Find the range of the following function

1. mathmath333

\large \color{black}{\begin{align}f(x)=2-3x,\ x\in \mathbb{R},\ x>0 \hspace{.33em}\\~\\ \end{align}}

2. geerky42

Can you graph 2-3x?

3. mathmath333

i cant use graph paper, i have to use pen and paper

4. acxbox22

you can still create a simple graph

5. geerky42

^

6. geerky42

|dw:1433027408780:dw|

7. geerky42

then label y-intercept and x-intercept, so you can have good idea of what graph would look like.

8. ikram002p

:O

9. mathmath333

|dw:1433027676752:dw|

10. zzr0ck3r

You could also find the domain of the inverse with the given restrictions.

11. mathmath333

what to do next @geerky42 after graphing

12. acxbox22

well the line crosses the y axis at (0,4) and it asks for range when x is greater than 0 and range means all the y-values the graph goes through

13. geerky42

Good, now what would graph look like with restriction of x>0? Once you figured that part, you should be able to tell what range is.

14. geerky42

|dw:1433028061222:dw|

15. geerky42

f(x) doesn't exist for any x-value smaller than 0, so with this restriction , you would only see that red line. And we know that 2-3x crosses y-axis at (0,2). Can you tell me what range is?

16. mathmath333

At axboxx the y intecept is at (0,2) not (0,4)

17. geerky42

|dw:1433028328277:dw|

18. acxbox22

|dw:1433028327298:dw|

19. acxbox22

yes sorry it should be (0,2)

20. mathmath333

|dw:1433028410647:dw|

21. geerky42

Range is set of possible y-values. From graph, you can see that y-values can only be smaller than 2, right?

22. mathmath333

yes

23. geerky42

So do you know the answer now?

24. mathmath333

$$x\leq 2$$

25. acxbox22

range isn't a coordinate but a set of values

26. acxbox22

are you sure it is less than or equal to? it says x>0 not x>=0..

27. mathmath333

$$y\leq 2$$

28. acxbox22

yes and...??

29. mathmath333

how do i know if it is less than equal to or equal to

30. geerky42

If x=0 is NOT included, then f(0) = 2-3(0) shouldn't be included in range as well.

31. acxbox22

|dw:1433028867299:dw|

32. mathmath333

and how to write this range in standard form

33. mathmath333

i mean notation form

34. geerky42

Since it doesn't include 2 and it goes all the way to negative infinity, you would have $$(-\infty, 2)$$

35. geerky42

If 2 IS included, then you would have $$\large (-\infty, 2]$$

36. acxbox22

or you can write it as |dw:1433029288104:dw|

37. mathmath333

u mean |dw:1433029404671:dw|

38. mathmath333

ok thnks both

39. freckles

you can also do this: $x>0 \\ \text{ multiply both sides by -3 } \\ -3x<0 \\ \text{ now add 2 on both sides } 2-3x<2 \\ y=2-3x \\ \text{ so we have } \\ y<2$

40. mathmath333

wow that looks cool