Question

I really need help with finding the average rate of change. Can someone please help me??

Answer 1

post the problem and I shall try!

Answer 2

Sure, Jon. What's the function? and on what interval are we trying to find the average rate of change?

Answer 3

Use the graph below to answer the following question.

What is the average rate of change from x = -1 to x = 1?

A. -4

B. -2

C. 2

D. 4

I know the average rate of change formula is --> \[A(x)=\frac{ f(x)-f(a) }{ x-a }\]

But I have no clue how to plug in the numbers or the process.

Answer 4

Jon: The interval of interest is [-1,1]. Please evaluate f(x) at each value. Yes, I know that the function is not given as an algebraic expression, but you can obtain the y-values directly from the graph for each x=-1 and x=1. What are they? f(1)=? f(-1)=?

Answer 5

(-1,0) (1,0) ??

Answer 6

Hold a moment, please.

Answer 7

okay

Answer 8

Jon: I did some quick calculations and have found that the equation of this parabola is y=(x-2)-3. Please evaluate this function at x=1 and again at x=-1.

Answer 9

what do you mean evaluate it?

Answer 10

"evaluate" is a command that means "find the value of."
The equation of the parabola shown in your diagram is y=(x-2)^2-3. I am asking you to substitute x=1 and then x=-1 to determine the y value for each of those x values. That's what I mean when I ask you to "evaluate the function at 1 and -1."

Answer 11

okay, give me a minute to work it out.

Answer 12

y=6 and y=-2 ??

Answer 13

Working on it; I need to check something; I'll be right with you.

Answer 14

okay.

Answer 15

Many apologies. My own equation for the parabola was wrong. It should be y=(x-1)^2-3. So sorry. Please evaluate this new equation at both 1 and -1.

Answer 16

okay, one second....

Answer 17

I got y=1 and y=-3

Answer 18

Great. So, if x=1, y=-3, and if x=-1, y=1. Now please go back to that graph that you posted and determine for yourself whether or not the graph says the same thing about the values of y at x=1 and x=-1.

Answer 19

Jon, sorry to have to squash that, but your initial results were correct and your later results were not. Please look at the graph as I've asked.

Answer 20

Jon: Looking at the graph: If x = -1, what y value corresponds to that x?

Answer 21

2 ??

Answer 22

Locate x=-1 on the x-axis and then move straight up until you hit the graph. y=1 there. Please verify this for yourself. Now do the same for x=1. If x=1, y=??

Answer 23

I'm so dumb. I forgot to fix the parabola equation on the graphing program I'm using....

Answer 24

The formula for "average value of a function on the interval [a,b]" is\[Ave=\frac{ f(b)-f(a) }{ b-a }.\]
In this case your b = 1 and your a = -1.
Thus, you want \[Ave=\frac{ f(1)-f(-1) }{ 1-[-1] }\]
Using the y -values you've just found algebraically and from the graph, please find Ave.
Hint: f(1)=-3.

Answer 25

Jon, you provided a nice illustration of this function when you presented the problem. If you're more comfortable using your calculator, fine, but I'd prefer you get the info (y-values) directly from the graph you initially gave me.

Answer 26

Jon, hate to rush you, but we need to move faster on this. I need to get off the computer very soon. Please, check the graph again and see whether or not you agree on the following: y=1 when x=-1; y=-3 when x=1.

Answer 27

Sorry, Jon, I'm getting off the computer now. If you're interested, try to complete this problem, and, if you wish, message me when you're ready to resume work. Nice working with you. So long.

Answer 28

Thank you for helping!!!!! I really appreciate it.