Question

Find the average rate of change for the given function from x = -1 to x = 2

Use the table below:

x = -1 y = -3
x = 0 y = -1
x = 2 y = 3

Please help. I've been on this for a while. Thanks!

Answer 1

Average rate of change is the slope of the secant line connecting the two points on the graph. Difference in Y over difference in X for y(x)
\[Ave~rate~change = \frac{ y(2) - y(-1) }{ 2-(-1) }\]

Answer 2

Can you guide me through it? Do I just put the values into the formula?

Answer 3

For the function y(x)
y(2) = 3
y(-1) = -3

Answer 4

From the table

Answer 5

Would the average rate of change be 2? I'm a bit confused.

Answer 6

\[Ave~rate~change = \frac{ y(2) - y(-1) }{ 2-(-1) } = \frac{ 3 - (-3) }{ 2 - (-1) } = \]

Answer 7

right, 6 / 3 = 2

Answer 8

Ohh... ok. I kind of get it. So the correct answer would be 2? Confirmed? Just making sure.

Answer 9

For 2 points: (x , y(x)) and (x1 , y(x1))

\[ave~rate~change=\frac{ y(x) - y(x1) }{ x - x1 }\]

Answer 10

\[Ave~rate~change = \frac{ y(2) - y(-1) }{ 2-(-1) } = \frac{ 3 - (-3) }{ 2 - (-1) } =\frac{ 6 }{ 3 } = 2\]

Answer 11

Ok, that's better. I wanted to see a full "analysis" to make sure. A medal for you sir! Thanks.

Answer 12

Welcome, anytime