x g(x)
−2 2
−1 −3
0 2
1 17
Which of the following is a true statement for this function?
The function is increasing from x = −2 to x = −1.
The function is increasing from x = 0 to x = 1.
The function is decreasing from x = −1 to x = 0.
The function is decreasing from x = 0 to x = 1.

- anonymous

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- anonymous

I think its A

- anonymous

@LynFran

- anonymous

@Luigi0210

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## More answers

- anonymous

it's the second one, because the output of 0=2 and the output of 1=17, so it is increasing from 0 to 1

- anonymous

Okay, thanks!

- anonymous

you're welcome :P

- anonymous

Water coming out from a fountain is modeled by the function f(x) = −x2 + 6x + 6 where f(x) represents the height, in feet, of the water from the fountain at different times x, in seconds.
What does the average rate of change of f(x) from x = 2 to x = 5 represent?
The water travels an average distance of 4 feet from 2 seconds to 5 seconds.
The water travels an average distance of 1 foot from 2 seconds to 5 seconds.
The water falls down with an average speed of 2 feet per second from 2 seconds to 5 seconds.
The water falls down with an average speed of 1 foot per second from 2 seconds to 5 seconds. @Nnesha

- anonymous

make sure to medal XD

- anonymous

I think the second one is D? I am just trying to check my answers ><

- anonymous

If D was correct then it would make A true also... i'm pretty sure XD. From 2-5 seconds it would be a total of 4 seconds so if the water it traveling at 1 foot per second for 4 seconds, it would be a total of 4 feet.

- anonymous

i think

- Nnesha

average rate of change means slope
the formula to find slope is \[\huge\rm \frac{ y_2 -y_1 }{ x_2 -x_1 }\]
given x=2 x=5
you have to find f(5) and f(2)
so substitute x for 5 into f(x) function to find y

- Nnesha

\[\huge\rm f(x) = −x^2 + 6x + 6\] replace x with 5 and then with 2 solve let me know what you get

- anonymous

f(x)=61
f(x)=22

- Nnesha

nope try again

- Nnesha

remember it's x^2 so it would be (2)^2

- anonymous

So, would the number be negative? I confused now lol

- Nnesha

show ur work how did you replaced x with 2 ?

- anonymous

f(x)=-2^2 +6 x 2 + 6?

- Nnesha

yes right

- anonymous

So, then f(x)=-4+6 x 2 + 6?

- anonymous

I see, they were supposed to remain negative

- Nnesha

yes right!
so final answer is what

- anonymous

f(x)=-4 plus 12 plus 6
f(x)=8 plus 6
f(x)=14

- Nnesha

yes right
now replace x with 5

- anonymous

f(x)=-25 plus 30 plus 6
f(x) = 5 plus 6
f(x)=11

- Nnesha

yes right so order pairs are ( 2,14)(5,11)
now plug them into the slope formula

- anonymous

2^2-5^1
over
14^2 -11^1

- Nnesha

ohh wait
Y-2 means 2nd y not square

- Nnesha

\[\huge\rm (x_1 ,y_1) (1st ~x , 1st ~y)\]

- anonymous

wait what

- Nnesha

\(\color{blue}{\text{Originally Posted by}}\) @gigirained
2^2-5^1
over
14^2 -11^1
\(\color{blue}{\text{End of Quote}}\)
it's not 14^2

- Nnesha

|dw:1441384007239:dw|

- Nnesha

\[\huge\rm \frac{\color{reD}{ y_2} -y_1 }{ x_2 -x_1 }\]
y_2 is just 11

- anonymous

Ohh okay

- Nnesha

so same with x_2 and x_1 substitute

- anonymous

2-5
over
14 -11

- anonymous

?

- Nnesha

x should be at the denomiantor

- Nnesha

denominator *

- Nnesha

\(\color{blue}{\text{Originally Posted by}}\) @gigirained
2-5
over
14 -11
\(\color{blue}{\text{End of Quote}}\)
just flip it!

- anonymous

Oh, alright, sorry i went to get water

- Nnesha

lol

- Nnesha

water is already in ur question lol solve that you will get the water

- anonymous

haha, nice one

- anonymous

so, i subtract and then divide or?

- Nnesha

yes subtract then divide
PEMDAS rules!

- anonymous

so then, 14-11=3 and 2-5=-3
3/-3=-1?

- Nnesha

yes right that's average rate
it's negative so water would decrease or increase ?

- anonymous

decrease

- Nnesha

yes right !

- Nnesha

falls down ugh samething

- anonymous

lol yea

- Nnesha

alright good to go! good luck!

- anonymous

Thank you!

- Nnesha

np!

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