What is the average rate of change for the sequence shown below? a coordinate plane showing the points negative 1, 4. 1, 3. 3, 2. 5, 1.

- 1/2 = - 0.5

Explanation:

1. Make the sequence clear. These are the given points (x,y):

2. The average rate of change only takes into account the last and the first pairs of your intervals, those are (5, 1) and (-1, 4).

Average rate of change = [change in y] / [change in x] = [1 - 4] / [5 - (-1) ] =

  = - 3 / 6 = - 1/2 = - 0.5  ← answer

The averate ratre of change is the slope of the line that joins the first and last points. The fact that the result is negative means that there was a net decrease of the values.

3< x< 5

step-by-step explanation:

|x - 4| < 1

there are two solutions, one positive and one negative.   remember to flip the inequality when taking the negative solution

x-4 < 1       x-4 > -1

add 4 to each side

x-4+4 < 1+4       x-4+4 > -1+4

x< 5                 x> 3

3< x< 5