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

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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0\(\large \color{black}{\begin{align}f(x)=23x,\ x\in \mathbb{R},\ x>0 \hspace{.33em}\\~\\ \end{align}}\)

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0i cant use graph paper, i have to use pen and paper

acxbox22
 one year ago
Best ResponseYou've already chosen the best response.3you can still create a simple graph

geerky42
 one year ago
Best ResponseYou've already chosen the best response.3dw:1433027408780:dw

geerky42
 one year ago
Best ResponseYou've already chosen the best response.3then label yintercept and xintercept, so you can have good idea of what graph would look like.

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0dw:1433027676752:dw

zzr0ck3r
 one year ago
Best ResponseYou've already chosen the best response.0You could also find the domain of the inverse with the given restrictions.

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0what to do next @geerky42 after graphing

acxbox22
 one year ago
Best ResponseYou've already chosen the best response.3well 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 yvalues the graph goes through

geerky42
 one year ago
Best ResponseYou've already chosen the best response.3Good, 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
 one year ago
Best ResponseYou've already chosen the best response.3dw:1433028061222:dw

geerky42
 one year ago
Best ResponseYou've already chosen the best response.3f(x) doesn't exist for any xvalue smaller than 0, so with this restriction , you would only see that red line. And we know that 23x crosses yaxis at (0,2). Can you tell me what range is?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0At axboxx the y intecept is at (0,2) not (0,4)

geerky42
 one year ago
Best ResponseYou've already chosen the best response.3dw:1433028328277:dw

acxbox22
 one year ago
Best ResponseYou've already chosen the best response.3dw:1433028327298:dw

acxbox22
 one year ago
Best ResponseYou've already chosen the best response.3yes sorry it should be (0,2)

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0dw:1433028410647:dw

geerky42
 one year ago
Best ResponseYou've already chosen the best response.3Range is set of possible yvalues. From graph, you can see that yvalues can only be smaller than 2, right?

geerky42
 one year ago
Best ResponseYou've already chosen the best response.3So do you know the answer now?

acxbox22
 one year ago
Best ResponseYou've already chosen the best response.3range isn't a coordinate but a set of values

acxbox22
 one year ago
Best ResponseYou've already chosen the best response.3are you sure it is less than or equal to? it says x>0 not x>=0..

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0how do i know if it is less than equal to or equal to

geerky42
 one year ago
Best ResponseYou've already chosen the best response.3If x=0 is NOT included, then f(0) = 23(0) shouldn't be included in range as well.

acxbox22
 one year ago
Best ResponseYou've already chosen the best response.3dw:1433028867299:dw

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0and how to write this range in standard form

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0i mean notation form

geerky42
 one year ago
Best ResponseYou've already chosen the best response.3Since it doesn't include 2 and it goes all the way to negative infinity, you would have \((\infty, 2)\)

geerky42
 one year ago
Best ResponseYou've already chosen the best response.3If 2 IS included, then you would have \(\large (\infty, 2]\)

acxbox22
 one year ago
Best ResponseYou've already chosen the best response.3or you can write it as dw:1433029288104:dw

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0u mean dw:1433029404671:dw

freckles
 one year ago
Best ResponseYou've already chosen the best response.0you can also do this: \[x>0 \\ \text{ multiply both sides by 3 } \\ 3x<0 \\ \text{ now add 2 on both sides } 23x<2 \\ y=23x \\ \text{ so we have } \\ y<2\]

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0wow that looks cool
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