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mathmath333

  • one year ago

Find the range of the following function

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  1. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align}f(x)=2-3x,\ x\in \mathbb{R},\ x>0 \hspace{.33em}\\~\\ \end{align}}\)

  2. geerky42
    • one year ago
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    Can you graph 2-3x?

  3. mathmath333
    • one year ago
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    i cant use graph paper, i have to use pen and paper

  4. acxbox22
    • one year ago
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    you can still create a simple graph

  5. geerky42
    • one year ago
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    ^

  6. geerky42
    • one year ago
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    |dw:1433027408780:dw|

  7. geerky42
    • one year ago
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    then label y-intercept and x-intercept, so you can have good idea of what graph would look like.

  8. ikram002p
    • one year ago
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    :O

  9. mathmath333
    • one year ago
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    |dw:1433027676752:dw|

  10. zzr0ck3r
    • one year ago
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    You could also find the domain of the inverse with the given restrictions.

  11. mathmath333
    • one year ago
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    what to do next @geerky42 after graphing

  12. acxbox22
    • one year ago
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    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
    • one year ago
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    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
    • one year ago
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    |dw:1433028061222:dw|

  15. geerky42
    • one year ago
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    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
    • one year ago
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    At axboxx the y intecept is at (0,2) not (0,4)

  17. geerky42
    • one year ago
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    |dw:1433028328277:dw|

  18. acxbox22
    • one year ago
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    |dw:1433028327298:dw|

  19. acxbox22
    • one year ago
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    yes sorry it should be (0,2)

  20. mathmath333
    • one year ago
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    |dw:1433028410647:dw|

  21. geerky42
    • one year ago
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    Range is set of possible y-values. From graph, you can see that y-values can only be smaller than 2, right?

  22. mathmath333
    • one year ago
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    yes

  23. geerky42
    • one year ago
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    So do you know the answer now?

  24. mathmath333
    • one year ago
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    \(x\leq 2\)

  25. acxbox22
    • one year ago
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    range isn't a coordinate but a set of values

  26. acxbox22
    • one year ago
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    are you sure it is less than or equal to? it says x>0 not x>=0..

  27. mathmath333
    • one year ago
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    \(y\leq 2\)

  28. acxbox22
    • one year ago
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    yes and...??

  29. mathmath333
    • one year ago
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    how do i know if it is less than equal to or equal to

  30. geerky42
    • one year ago
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    If x=0 is NOT included, then f(0) = 2-3(0) shouldn't be included in range as well.

  31. acxbox22
    • one year ago
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    |dw:1433028867299:dw|

  32. mathmath333
    • one year ago
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    and how to write this range in standard form

  33. mathmath333
    • one year ago
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    i mean notation form

  34. geerky42
    • one year ago
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    Since it doesn't include 2 and it goes all the way to negative infinity, you would have \((-\infty, 2)\)

  35. geerky42
    • one year ago
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    If 2 IS included, then you would have \(\large (-\infty, 2]\)

  36. acxbox22
    • one year ago
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    or you can write it as |dw:1433029288104:dw|

  37. mathmath333
    • one year ago
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    u mean |dw:1433029404671:dw|

  38. mathmath333
    • one year ago
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    ok thnks both

  39. freckles
    • one year ago
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    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
    • one year ago
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    wow that looks cool

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