Given the function, fx) = x2-3, calculate the average rate of change of the function from x = 1 to x = 3. -2
4
8
-12

The average rate of change is 4.

Step-by-step explanation:

We are given the function:

And we want to find the average rate of change from x = 1 to x = 3.

The average rate of change is synonymous with the slope. So, we can evaluae the endpoints and find the slope between them.

The first endpoint is:

The second endpoint is:

This yields the two poins (1, -2) and (3, 6). The slope between them will be:

Hence, the average rate of change is 4.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for