Find the range of the following function

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Find the range of the following function

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\(\large \color{black}{\begin{align}f(x)=2-3x,\ x\in \mathbb{R},\ x>0 \hspace{.33em}\\~\\ \end{align}}\)
Can you graph 2-3x?
i cant use graph paper, i have to use pen and paper

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Other answers:

you can still create a simple graph
^
|dw:1433027408780:dw|
then label y-intercept and x-intercept, so you can have good idea of what graph would look like.
:O
|dw:1433027676752:dw|
You could also find the domain of the inverse with the given restrictions.
what to do next @geerky42 after graphing
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
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.
|dw:1433028061222:dw|
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?
At axboxx the y intecept is at (0,2) not (0,4)
|dw:1433028328277:dw|
|dw:1433028327298:dw|
yes sorry it should be (0,2)
|dw:1433028410647:dw|
Range is set of possible y-values. From graph, you can see that y-values can only be smaller than 2, right?
yes
So do you know the answer now?
\(x\leq 2\)
range isn't a coordinate but a set of values
are you sure it is less than or equal to? it says x>0 not x>=0..
\(y\leq 2\)
yes and...??
how do i know if it is less than equal to or equal to
If x=0 is NOT included, then f(0) = 2-3(0) shouldn't be included in range as well.
|dw:1433028867299:dw|
and how to write this range in standard form
i mean notation form
Since it doesn't include 2 and it goes all the way to negative infinity, you would have \((-\infty, 2)\)
If 2 IS included, then you would have \(\large (-\infty, 2]\)
or you can write it as |dw:1433029288104:dw|
u mean |dw:1433029404671:dw|
ok thnks both
you can also do this: \[x>0 \\ \text{ multiply both sides by -3 } \\ -3x<0 \\ \text{ now add 2 on both sides } 2-3x<2 \\ y=2-3x \\ \text{ so we have } \\ y<2\]
wow that looks cool

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