Question

Help with functions?

Answer 1

@jim_thompson5910 @phi @Nnesha

Answer 2

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?

Answer 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)

Answer 4

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 ?

Answer 5

I'm not sure if I understand..

Answer 6

for the f(x) (the graph)
can you read the "y" value at x=-1 ?

Answer 7

I mean g(x) graph

Answer 8

Yeah it's -1? ..right?

Answer 9

Wait nooo

Answer 10

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

Answer 11

Sorry had I quadrants mixed up.

Answer 12

-2!

Answer 13

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

Answer 14

0?

Answer 15

Er -2?

Answer 16

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)

Answer 17

not er -2, you did it correctly the first time.

Answer 18

Okay yeah sorry. Haven't been focusing on math for a couple days (trying to reach my end date)

Answer 19

Let's do h(x)
what is y at x= -1 and y at x= 3 ?

Answer 20

-2 and 0?

Answer 21

Oh wrong one!!

Answer 22

h(x): 14 and 62?

Answer 23

yes, and what is the "change in y" ?

Answer 24

i.e. when we go from 14 up to 62, how much did y change ?

Answer 25

It goes up by 5, 7, 9...

Answer 26

we want a single number. if you start at 14 and end up at 62, how far did you go up ?

Answer 27

So the difference is 48.

Answer 28

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.

Answer 29

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 = ?

Answer 30

2!

Answer 31

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

Answer 32

Pluggin in x=3? That would be 34.

Answer 33

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.

Answer 34

g(x), h(x), and f(x)?

Answer 35

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?

Answer 36

OH g, f and h.

Answer 37

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

Answer 38

Right. So is that right?

Answer 39

yes, that is it.

Answer 40

Okay awesome. Thank you so so much! I'm so ready to be done with Algebra II.

Answer 41

Think of it as a life-altering experience, and once in a life-time adventure.

Answer 42

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)