Please help, Algebra II - Will Fan and Medal.

- Xaze

Please help, Algebra II - Will Fan and Medal.

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- Xaze

Compare the functions shown below:

- Xaze

##### 1 Attachment

- Xaze

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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## More answers

- anonymous

the rate of change of that line is a constant
it is the slope
do you know it?

- Xaze

@satellite73 Would 0.5/3 be the slope? I'm pretty bad at this, haha

- Xaze

Sorry, 1.5*/3

- Astrophysics

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|

- Astrophysics

So what is f(3) for f(x)?

- Xaze

f(3)=((3)+3)^2-2, am I doing okay, so far?

- Astrophysics

Yup, exactly!

- Xaze

f(3)=(9)^2-2 - > f(3)=81-2 -> 79?

- Astrophysics

Not quite, 3+3 = 6 :P

- Xaze

Oh whoops... I was thinking of multiplication, for some reason.. f(3)=(6)^2-2 -> f(3)=36-2 - > f(3)=34?

- Astrophysics

Yup that's good!

- Astrophysics

now find f(-1)

- Xaze

Yay! ^^

- Astrophysics

@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

- Xaze

|dw:1440381614071:dw|

- Astrophysics

perfect now we have \[f(x) = \frac{ 34-2 }{ 3-(-1) }\]

- Xaze

\[f(x)=32/4?\]

- Astrophysics

Yes simplify it

- Astrophysics

I should say m = that not f(x) xD but same thing

- Xaze

16/2

- Astrophysics

m = 34/4 = 16/2 keep going

- Xaze

8/1

- Astrophysics

Yup m = 8 for f(x)

- Astrophysics

|dw:1440378413551:dw| what are these two points?

- Astrophysics

We're doing g(x) now

- Xaze

Computer is slowing down - sorry, sorry x-x The two points are (-1,-2) and (3,0)

- Astrophysics

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

- Xaze

All right... |dw:1440382384897:dw|

- Astrophysics

Yes! 1/2 is good

- Astrophysics

So we have slope for f(x) = 8, g(x) = 1/2, now lets find the slope for h(x)

- Xaze

Not sure how to find the slope for that one... doesn't seem to be in my notes

- Astrophysics

Just read the table and apply the formula

- Astrophysics

|dw:1440379170633:dw|

- Xaze

The formula \[m=y2-y1/x2-x1\]? Just making sure

- Astrophysics

yup

- Xaze

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?

- Astrophysics

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

- Xaze

|dw:1440383049367:dw|

- Astrophysics

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

- Xaze

g(x),f(x), h(x)!

- Astrophysics

Looks good :)

- Xaze

Thanks so much, you're really a life-saver!

- Astrophysics

Yw :)

- Xaze

@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...

- Astrophysics

Oh this was a test...we can't help on tests sorry.

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