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@jim_thompson5910 @phi @Nnesha
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?
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)
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..
for the f(x) (the graph) can you read the "y" value at x=-1 ?
I mean g(x) graph
Yeah it's -1? ..right?
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.
yes. now what is the y value at x= 3 ?
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)
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)
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?
yes, and what is the "change in y" ?
i.e. when we go from 14 up to 62, how much did y change ?
It goes up by 5, 7, 9...
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.
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.
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 = ?
and now for x=3 . can you do that?
Pluggin in x=3? That would be 34.
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)?
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.
we could divide each by 4, but the order won't change.
Right. So is that right?
yes, that is it.
Okay awesome. Thank you so so much! I'm so ready to be done with Algebra II.
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)