Please help, Algebra II - Will Fan and Medal.

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Please help, Algebra II - Will Fan and Medal.

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What is the correct order of the functions from least to greatest according to the average rate of change on the interval from x = -1 to x = 3?

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the rate of change of that line is a constant it is the slope do you know it?
@satellite73 Would 0.5/3 be the slope? I'm pretty bad at this, haha
Sorry, 1.5*/3
You have to find the slope of each function f(x), g(x), and h(x) \[A(x)= \frac{ f(b)-f(a) }{ b-a }\] this is the average rate of change |dw:1440377631421:dw|
So what is f(3) for f(x)?
f(3)=((3)+3)^2-2, am I doing okay, so far?
Yup, exactly!
f(3)=(9)^2-2 - > f(3)=81-2 -> 79?
Not quite, 3+3 = 6 :P
Oh whoops... I was thinking of multiplication, for some reason.. f(3)=(6)^2-2 -> f(3)=36-2 - > f(3)=34?
Yup that's good!
now find f(-1)
Yay! ^^
@satellite73 hey if you want to take an image and upload it on draw which is very useful check out this guide on how to do it http://openstudy.com/users/astrophysics#/updates/55921cb5e4b0c2028eab5952 it's really quick to get it and helpful :P
|dw:1440381614071:dw|
perfect now we have \[f(x) = \frac{ 34-2 }{ 3-(-1) }\]
\[f(x)=32/4?\]
Yes simplify it
I should say m = that not f(x) xD but same thing
16/2
m = 34/4 = 16/2 keep going
8/1
Yup m = 8 for f(x)
|dw:1440378413551:dw| what are these two points?
We're doing g(x) now
Computer is slowing down - sorry, sorry x-x The two points are (-1,-2) and (3,0)
Yup perfect, so use \[m = \frac{ y_2-y_1 }{ x_2-x_1 }\] to find the slope |dw:1440378607899:dw| this is what it means visually
All right... |dw:1440382384897:dw|
Yes! 1/2 is good
So we have slope for f(x) = 8, g(x) = 1/2, now lets find the slope for h(x)
Not sure how to find the slope for that one... doesn't seem to be in my notes
Just read the table and apply the formula
|dw:1440379170633:dw|
The formula \[m=y2-y1/x2-x1\]? Just making sure
yup
Okay, before I solve, how did you know to get (-1,14) and (3,62) from the chart? Or did you pick them randomly... and any pair you choose would give the same slope?
No, because your question is asking for the average rate of change from x = -1 to x = 3, but it doesn't really matter, you'll get the same slope for any two points
|dw:1440383049367:dw|
Yes! Now we have the slopes f(x) = 8, g(x) = 1/2 and h(x) = 12 now put it least to greatest and we're done
g(x),f(x), h(x)!
Looks good :)
Thanks so much, you're really a life-saver!
Yw :)
@Astrophysics, Do you think you can help with a few more? I'm almost finished with this test and I've got to get it submitted before midnight...
Oh this was a test...we can't help on tests sorry.

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