Question

I need Help!!! i will give you a medal if you help me!
Compare the functions shown below:


f(x) = (x + 3)2 - 2
g(x)

linear graph with y intercept of negative 1 over 2 and x intercept of 3
h(x)

x y
-3 2
-2 7
-1 14
0 23
1 34
2 47
3 62


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 1

these are the choices
f(x), g(x), h(x)

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

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

g(x), h(x), f(x)
i think its the second one but im not sure it could be the third one.

Answer 2

@ilikemath50 can you help me please!!!!!

Answer 3

I will need to see the actual graph to answer that

Answer 4

@ilikemath50 ok hold up

Answer 5

is this FLVS?

Answer 6

I really think its b but i would like to know what you get.

Answer 7

this is a hard one.. @precal @waterineyes @thomaster @Abhisar @abb0t @SolomonZelman

Answer 8

I don't think I can help with this, sorry :(

Answer 9

@ilikemath50 its ok thanks though.

Answer 10

@aum do you think b is correct?

Answer 11

I can't just give out answers but I can help finding the answer.

Average rate of change of f(x) on the interval from x = -1 to x = 3 is:

\( \Large
\frac{f(3) - f(-1)}{(3-(-1))} = \frac{f(3) - f(-1)}{4} \)

Answer 12

ok, so whats next?

Answer 13

@aum

Answer 14

so b wasn't right?

Answer 15

Find the equation of h(x). It is a straight line and you are given the x and y intercepts.

\(\Large
\frac{x}{a} + \frac{y}{b} = 1
\)
is the equation of a straight line with x-intercept of 'a' and a y-intercept of 'b'.

Answer 16

I haven't worked out the problem. There are several steps involved and we have to go through each step before we can arrive at the answer.

Answer 17

ohh ok. well h(x) average rate of change is 6 right?

Answer 18

@aum

Answer 19

For g(x) average rate of change is:1/6

Answer 20

ok so what do we do next? @aum

Answer 21

Did you find average rate of change for f(x) first?

Answer 22

no i didn't. @aum

Answer 23

how do i find it?

Answer 24

That should be done first before we can proceed to the next step.

Answer 25

I have given the formula in my very first reply.

Answer 26

so is it f(4)/4 which equals 1? @aum

Answer 27

f(x) = (x + 3)^2 - 2
Find f(3) by putting x = 3 on the right hand side.
Find f(-1) by putting x = -1 on the right hand side.
Then plug the numbers into the formula in my first reply.

Answer 28

ok hold on.

Answer 29

f(3)= 34 and f(-1) = 0 right?

Answer 30

f(-1) =2

Answer 31

correct. f(3) = 34; f(-1) = 2. plug it into the formula

Answer 32

yay! lol ok so is it 26?

Answer 33

(34 - 2) / 4 = 32 / 4 = 8.

Answer 34

i had just got that. sorry i had did it wrong.

Answer 35

For the second function, simply find the slope of the straight line.
That will be the average rate of change.
In this case, slope = y-intercept / x-intercept = ?

Answer 36

ok what would be the y-intercept though?

Answer 37

For g(x) the problem says: "linear graph with y intercept of negative 1 over 2 and x intercept of 3"

Answer 38

the x would be 3 right?

Answer 39

y-intercept = -1/2
x-intercept = 3

y-intercept / x-intercept = ?

Answer 40

ok hold on

Answer 41

@aum i got 0.16

Answer 42

-0.16

Answer 43

Yes, -0.16.

For the last function, read the numbers off the table.
Find h(3).
Find h(-1)

Plug it into the formula in my first reply (except f(x) now refers to h(x) in the formula)

Answer 44

is it 12 @aum

Answer 45

Correct!

So we have the following average rate of change:
f(x): 8
g(x): -0.16
h(x): 12

Arrange from lowest to highest.

Answer 46

whoaaaaa! lol ok so its g(x), f(x), h(x) @aum

Answer 47

Correct!

Answer 48

And I did not find out the answer any sooner than you did.

Answer 49

so it was b! lol Thank You so much!!!!!

Answer 50

You are welcome.

Answer 51

aww thanks for the medal, you are good at what you do!!!

Answer 52

@aum

Answer 53

Oh, thanks. Glad to be able to help.