mathmath333
  • mathmath333
Find the range of the following function
Mathematics
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
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.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
mathmath333
  • mathmath333
\(\large \color{black}{\begin{align}f(x)=2-3x,\ x\in \mathbb{R},\ x>0 \hspace{.33em}\\~\\ \end{align}}\)
geerky42
  • geerky42
Can you graph 2-3x?
mathmath333
  • mathmath333
i cant use graph paper, i have to use pen and paper

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

acxbox22
  • acxbox22
you can still create a simple graph
geerky42
  • geerky42
^
geerky42
  • geerky42
|dw:1433027408780:dw|
geerky42
  • geerky42
then label y-intercept and x-intercept, so you can have good idea of what graph would look like.
ikram002p
  • ikram002p
:O
mathmath333
  • mathmath333
|dw:1433027676752:dw|
zzr0ck3r
  • zzr0ck3r
You could also find the domain of the inverse with the given restrictions.
mathmath333
  • mathmath333
what to do next @geerky42 after graphing
acxbox22
  • 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
geerky42
  • 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.
geerky42
  • geerky42
|dw:1433028061222:dw|
geerky42
  • 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?
mathmath333
  • mathmath333
At axboxx the y intecept is at (0,2) not (0,4)
geerky42
  • geerky42
|dw:1433028328277:dw|
acxbox22
  • acxbox22
|dw:1433028327298:dw|
acxbox22
  • acxbox22
yes sorry it should be (0,2)
mathmath333
  • mathmath333
|dw:1433028410647:dw|
geerky42
  • geerky42
Range is set of possible y-values. From graph, you can see that y-values can only be smaller than 2, right?
mathmath333
  • mathmath333
yes
geerky42
  • geerky42
So do you know the answer now?
mathmath333
  • mathmath333
\(x\leq 2\)
acxbox22
  • acxbox22
range isn't a coordinate but a set of values
acxbox22
  • acxbox22
are you sure it is less than or equal to? it says x>0 not x>=0..
mathmath333
  • mathmath333
\(y\leq 2\)
acxbox22
  • acxbox22
yes and...??
mathmath333
  • mathmath333
how do i know if it is less than equal to or equal to
geerky42
  • geerky42
If x=0 is NOT included, then f(0) = 2-3(0) shouldn't be included in range as well.
acxbox22
  • acxbox22
|dw:1433028867299:dw|
mathmath333
  • mathmath333
and how to write this range in standard form
mathmath333
  • mathmath333
i mean notation form
geerky42
  • geerky42
Since it doesn't include 2 and it goes all the way to negative infinity, you would have \((-\infty, 2)\)
geerky42
  • geerky42
If 2 IS included, then you would have \(\large (-\infty, 2]\)
acxbox22
  • acxbox22
or you can write it as |dw:1433029288104:dw|
mathmath333
  • mathmath333
u mean |dw:1433029404671:dw|
mathmath333
  • mathmath333
ok thnks both
freckles
  • freckles
you can also do this: \[x>0 \\ \text{ multiply both sides by -3 } \\ -3x<0 \\ \text{ now add 2 on both sides } 2-3x<2 \\ y=2-3x \\ \text{ so we have } \\ y<2\]
mathmath333
  • mathmath333
wow that looks cool

Looking for something else?

Not the answer you are looking for? Search for more explanations.