Question

What is the correct order of the functions from least to greatest according to the average rate of change on the interval from x = 0 to x = 4?

Answer 1

are you in calculus?

Answer 2

No algebra 2.

Answer 3

so the slope is the average rate of change over a given interval

Answer 4

what is the slope of the line in g(x)?

Answer 5

Ummm (2, -1) ???

Answer 6

for f(x) use the endpoint to compute the slope, that will be the average rate of change over that interval

Answer 7

slope is a fraction (well, rise over run)

Answer 8

Well, okay

Answer 9

\[\text{slope }=\frac{ \text{rise} }{ \text{run} }=\frac{ y_2-y_1 }{ x_2-x_1 }\]

Answer 10

f(x) . from 0->1 it changes 1. From 1->2 it changes 7. from 2->3 it changes 19 from 3->4 37. 1+7+19+37/4=16

Answer 11

pick 2 points on the line and you can find its slope using this formula

Answer 12

Ahhhh, okay I will try that

Answer 13

you can do the same for f(x), just pick the first and last points. then you'll get the average rate of change over those x values

Answer 14

Okay, thanks for all your help guys I appreciate it! :)

Answer 15

h(x)=(x+4)^2+2
for x=0, 18
for x=1, 27
for x=2, 38
for x=3, 51
for x=4, 66
those your value

Answer 16

for g(x) it totally depends on the interval. if you do it for the entire domain, then the average rate of change will be 0.

Answer 17

So the answer would be the last option right? Since g(x) has the lowest average rate of change?

Answer 18

average rate of change on h(x)=9+11+13+15/4=12

Answer 19

OH whoops I forgot to add the answer choices

Answer 20

what did you get for g(x) ?

Answer 21

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

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

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

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

Answer 22

I did f(x) and h(x), what was the slope of g(x)?

Answer 23

0

Answer 24

How did you get a slope of zero ?

Answer 25

why?

you'll have the points \(\left(-\infty,\infty\right) \text{ and }\left(\infty,\infty\right)\) which will give you
\[\text{slope}=\frac{ \infty-\infty }{\infty-\left( -\infty \right) }=\frac{ 0 }{ 2\infty }=0\]

Answer 26

Isn't 0 the change of rate?

Answer 27

rate of change...

Answer 28

why cant you use the points (0,-1) and (4,-3)

Answer 29

f(x) has an average rate of change of \[\frac{ 64-(-27) }{ 4-(-3) }=\frac{ 91 }{ 7 }=13\]

Answer 30

g(x) has an average rate of change of \[\frac{ 0-(-1) }{-2-0 }=-\frac{ 1 }{ 2 }\]

Answer 31

when you used -3,-27 that not in the interval ?

Answer 32

it only from x=0 to x=4

Answer 33

h(x) has an average rate of change (over its entire domain) of 0.

Answer 34

i realize that h(x) has that because with those points it is 0 too

Answer 35

oh, sorry. didn't see the caveat of the interval.

Answer 36

but on f(x) you used a value of x -3 to calculate rate of change in x=0-4 ?

Answer 37

f(x) has an average rate of change over [0,4] of\[\frac{ 64-0 }{ 4-0 }=\frac{ 64 }{4 }\]

Answer 38

which is 16 what i got

Answer 39

g(x) still has an average rate of change of \[-\frac{ 1 }{ 2 }\] because it's a line and the slope doesn't change

Answer 40

so it is f(x),g(x),h(x) correct

Answer 41

oh...whoops sorry yaaa I meant rate of change lol

Answer 42

h(x) has an average rate of change over [0, 4] of\[\frac{ 66-16 }{ 4-0 }=\frac{ 50 }{ 4}=12.5\]

Answer 43

wait i calculated rate of change on h(x) to be 12

Answer 44

so f(x), h(x), g(x) finally sorry for the confusion

Answer 45

That's not one of my options though.

Answer 46

oops, should be 66-18 over 4 which gives 12...
you are correct venny

Answer 47

so, g(x) is smallest, followed by h(x) then f(x), correct?

Answer 48

i also put it in opposite order of what was asked

Answer 49

pgpilot326 said the correct answer

Answer 50

YES! Thank you

Answer 51

good work

Answer 52

I wish I could give you both medals :(

Answer 53

it don't matter i am just here to help

Answer 54

I have two more problems! Are you both busy?

Answer 55

are they as hard as this one

Answer 56

we can all recip...then everyone gets one

Answer 57

Kind of...idk.

Answer 58

I can try but shouldnt we open new question ?

Answer 59

give yours to kendall and she can give one to me and then we're all good, but it really doesn't matter to me.

Answer 60

I'll post them & maybe yall can see if it's too difficult for yall or not

Answer 61

Yeah I'll open a new question.

Answer 62

yeah, i don't think they'll be too difficult