Question

Find the average rate of change for the given function from x = −3 to x = 1.

Answer 1

@annasjuice @helpme1.2

Answer 2

−1

−2

1

2

Answer 3

find the change in y as x goes from -3 to 1. the change in y / the change in x is the average rate of change.

Answer 4

@HelpBlahBlahBlah

Answer 5

how much does x change?

Answer 6

idk :(

Answer 7

draw a number line. mark x = -1. mark x = 3. how many units between x = -1 and x = 3?

Answer 8

-1 to 0
0 to 1
1 to 2
2 to 3

1 unit each. 4 units total, right?

Answer 9

sorry, -3 to 1. -3 to -2. -2 to -1. -1 to 0. 0 to 1. 4 units.

Answer 10

−1

−2

1

2
are my options

Answer 11

so the change in x is 4. Now look at the graph. find the y value at x = -3. find the y value at x = 1. how many units higher or lower? that's the change in y.

Answer 12

2. right?

Answer 13

okay, what are the coordinates of the point where x = -3?

Answer 14

i relly dont know im so lost right now

Answer 15

look at the graph. move along the x axis until you get to x = -3. can you find that point? go up or down until you run into the line on the graph. how many grid marks did you have to go up or down to get there?

Answer 16

4 over 1 up

Answer 17

starting at the point where the axes cross (0,0), we have to go 3 marks to the left to get to x = -3, and 1 mark up to get to the line. that means the coordinate of that spot is (-3,1).

now, to demonstrate that you understand, please find the coordinate of the point where x = 1

Answer 18

over 1 up 1

Answer 19

???/

Answer 20

can please tell me the answer and show me how u got there

Answer 21

@whpalmer4

Answer 22

@helpme1.2

Answer 23

no, isn't it over 1 and up 5? look at the markings on the y axis (the line that goes up and down).

Answer 24

so the coordinate there is (1,5) (it's always (x,y))

Answer 25

oh yes

Answer 26

so, at x = -3, the y value was 1. at x = 1, the y value is 5. what's the change in y?

Answer 27

@helpme1.2 please help me. i need the process and the answer

Answer 28

what is the difference between 1 and 5?!?

Answer 29

4

Answer 30

yes! so the change in y is +4, and the change in x is +4. the average rate of change is the change in y divided by the change in x. what is that?

Answer 31

is 1
!!!!

Answer 32

there you go! and you can see this if you look at the graph. each time you move one unit to the right along the x axis, the line goes up 1 unit, right?

Answer 33

if the average rate of change was 2, when you went 1 unit to the right, the line would go up 2 units. if the average rate of change was -1, when you went 1 unit to the right, the line would go DOWN 1 unit. really not so complicated — sounds like you need practice identifying points on the graph, though. that's a skill you'll need many, many, many times, so now's the time to learn it.

Answer 34

https://drive.google.com/file/d/0B5q8dbsgquFmZjJBUk1IRk9ZX1k/edit?usp=sharing

Answer 35

the reason I had him find the total change for x and y is that you can find the average rate of change for something other than a straight line that way. no need to learn new tricks later :-)