Help with functions?

- anonymous

Help with functions?

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- anonymous

@jim_thompson5910 @phi @Nnesha

- anonymous

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- anonymous

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

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 ?

- anonymous

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

- anonymous

Yeah it's -1? ..right?

- anonymous

Wait nooo

- phi

put your finger on -1 on the x-axis, and move your finger down until you hit the line

- anonymous

Sorry had I quadrants mixed up.

- anonymous

-2!

- phi

yes. now what is the y value at x= 3 ?

- anonymous

0?

- anonymous

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.

- anonymous

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 ?

- anonymous

-2 and 0?

- anonymous

Oh wrong one!!

- anonymous

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 ?

- anonymous

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 ?

- anonymous

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 = ?

- anonymous

2!

- phi

and now for x=3 . can you do that?

- anonymous

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.

- anonymous

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?

- anonymous

OH g, f and h.

- phi

we could divide each by 4, but the order won't change.

- anonymous

Right. So is that right?

- phi

yes, that is it.

- anonymous

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.

- anonymous

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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