Give the function f(x) = 3 ^ x - 4x determine the average rate of change from x = 1 x = 2

2

Step-by-step explanation:

Given the average rate of change formula, we must first find the x and y values of the function.

We are provided with the two x values, 1 and 2. We now need to find the output, or y.

ƒ(x)=3^x-4x

ƒ(1)=3-4=-1

ƒ(2)=9-8=1

Then, we use the formula (ƒ(2)-ƒ(1))/x2-x1(subscripts here, in case you multiplied) which gets us 2/1, or 2. Therefore, the average rate of change(ARC) is 2. I believe you just need to find the output and subtract if they are exactly one whole number apart, but don't quote me on that.

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.