Help with functions?

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Help with functions?

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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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A. f(x), g(x), h(x) B. g(x), f(x), h(x) C. h(x), g(x), f(x) D. g(x), h(x), f(x)
  • phi
you can do this by finding the change in y divided by the change in x the change in x fro -1 to 3 is 4 , and is the same for all 3 functions i.e. ignore dividing by 4, and just find the change in y can you do that ?
I'm not sure if I understand..
  • phi
for the f(x) (the graph) can you read the "y" value at x=-1 ?
  • phi
I mean g(x) graph
Yeah it's -1? ..right?
Wait nooo
  • phi
put your finger on -1 on the x-axis, and move your finger down until you hit the line
Sorry had I quadrants mixed up.
-2!
  • phi
yes. now what is the y value at x= 3 ?
0?
Er -2?
  • phi
yes. y=0 at x=3 and the "change in y" is 0 - (-2) = 2 (the average rate of change would be 2/4 = 1/2)
  • phi
not er -2, you did it correctly the first time.
Okay yeah sorry. Haven't been focusing on math for a couple days (trying to reach my end date)
  • phi
Let's do h(x) what is y at x= -1 and y at x= 3 ?
-2 and 0?
Oh wrong one!!
h(x): 14 and 62?
  • phi
yes, and what is the "change in y" ?
  • phi
i.e. when we go from 14 up to 62, how much did y change ?
It goes up by 5, 7, 9...
  • phi
we want a single number. if you start at 14 and end up at 62, how far did you go up ?
So the difference is 48.
  • phi
yes. and the slope (average rate of change ) is 48/4 (the 4 is the change in x from -1 to 3) so far we have g(x) slope is 2/4 and h(x) is 48/4 so g(x) should go before h(x) in your answer.
  • phi
now the first one f(x) = (x+3)^2 -2 we have to put in x=-1 and figure out f(-1) (-1+3)^2 -2 = ?
2!
  • phi
and now for x=3 . can you do that?
Pluggin in x=3? That would be 34.
  • phi
finally, change in y from 2 up to 34 is 32 the slope (average rate of change) for f(x) is 32/4 here is what we have for the slopes: f(x) is 32/4 g(x) slope is 2/4 h(x) is 48/4 now put them in order small to big.
g(x), h(x), and f(x)?
  • phi
ignore the divide by 4 you have f 32, g 2, and h 48 what is the smallest and which is the biggest? and which goes in the middle?
OH g, f and h.
  • phi
we could divide each by 4, but the order won't change.
Right. So is that right?
  • phi
yes, that is it.
Okay awesome. Thank you so so much! I'm so ready to be done with Algebra II.
  • phi
Think of it as a life-altering experience, and once in a life-time adventure.
True. I'm all for adventures, just not the one's where I have to figure out how many watermelons Kyle needs to sell (if you get my drift)

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