Question

Calculate the average rate of change for the given function, from x = 8 to x = 5.


x f(x)
8 0
5 4
−5 19

Answer 1

\[avg. rate of change = \frac{f(b) - f(a)}{b - a}\]

Answer 2

@iPwnBunnies i dont get it

Answer 3

The average rate of change will be y-values from one point to another point. Divided by the x-values of that point to the other point.

Answer 4

@iPwnBunnies meaning?

Answer 5

Meaning what the formula I wrote. It's just what it says. It's the average change in the slope between two points.

Answer 6

\[avg. rate of change = \frac{f(5) - f(8)}{5-8}\]

Answer 7

@iPwnBunnies

Answer 8

?

Answer 9

I literally gave you the formula and the set up. Isn't this a calculus problem, or at least a precalc problem?

Answer 10

no geometry

Answer 11

and @iPwnBunnies im trying to understand but its not easy

Answer 12

Sorry, I don't know how to explain it any better.

Answer 13

@BeautifulMelodies can you help and guide me through this?

Answer 14

Idk why you guys are doing rate of change in Geometry. You don't know the terms to understand what I'm saying.

Answer 15

@iPwnBunnies Im in ap classes and im only in 9th

Answer 16

So, I also took AP classes in 9th grade through high school. I'm not putting you down, it's just that you haven't learned concepts of slopes and rate of change put together yet because you're not at that level of math yet.

Answer 17

@iPwnBunnies and thats why im trying to get tutored and youre not helping because you are putting me down

Answer 18

This site is a quick way to help people who need an little push on a problem. I'm not a teacher, and I'm not gonna spend an hour via Internet attempting to teach something. I'm sorry if you feel that way.

Answer 19

you are very rude and disrepectful @iPwnBunnies if you dont have anything nice to say dont say it at all and consider yourself BLOCKED

Answer 20

I am sorry it took me so long to help you. My connection failed.

Answer 21

@BeautifulMelodies i really need help understanding this problem its really difficult for me

Answer 22

I really don't understand it either. But @AccessDenied might be able to help you.

Answer 23

@AccessDenied can you please help me?

Answer 24

So, what do you know about average rate of change so far? Anything particular not make sense?

Answer 25

when i did the calculations in my calculator its not accurate to the choice of answers
@AccessDenied

Answer 26

Calculations? What did you enter?

Answer 27

i entered 0-8/0-8

Answer 28

Like \( \dfrac{0 - 8}{0 - 8} \) ?

Answer 29

When we say, "rate of change", we are really looking at how much f(x) is changing over a change in x.
Like if I traveled 100 miles in a car. My trip took 5 hours. So my average rate of change is the change in distance I traveled (from 0 miles to 100 miles) per change in time (I start at 0 hours, up to 5 hours). This is equal to (100 - 0)mi / (5 - 0) hrs = 20 mph.
"Change" is a difference. The change between 10 and 15 is 15-10 = 5.
Does this make any sense?

Answer 30

@AccessDenied yes and a little

Answer 31

So in terms of f(x) and x, our rate of change is basically:
\( \text{Average rate of change} = \dfrac{\text{how much f(x) changes}}{\text{how much x changes}} \)
And as I said, "change" is the equivalent of differences. We subtract the final value from the first value to see how much the value changed.
Let's say we have a first x and a final x value. The "equation" takes this form:
\( \text{Average rate of change} = \dfrac{f(\text{final x}) - f(\text{initial x})}{\text{final x} - \text{initial x}} \)

Answer 32

In another sense, this is the equivalent of the slope of a line. The change in y per change in x is the slope.

Answer 33

@AccessDenied i got 19-0/-5-8 to 19/-13 and got 1.4615.... and the closest thing to that is 4/3

Answer 34

Now you have the right idea. Just notice that we wanted from x=8 to x=5. You used x=-5 and f(-5) instead of x=5 and f(5).

Answer 35

\( \dfrac{\color{red}{19} - 0}{\color{red}{-5} - 8} \) The average rate between x=-5 and x=8

\( \dfrac{\color{green}{4} - 0}{\color{Green}{5} - 8} \) The average rate between x= positive 5 and x=8
If you can see that small change, you should be fine.

Answer 36

ok thx i see it a @AccessDenied you were a big help :) Have a nice weekend

Answer 37

glad to help! and same to you. :)

Answer 38

I don't deserve a medal, it's k. Btw, blocking me just disallows messages between us. Good luck.