Option: C is the correct answer.
C.
Recursive Formula--
It is the formula which is used to represent the nth term of a sequence in terms of (n-1)th term of the sequence.
Here we are given a table of values by:
n f(n)
1 4
2 20
3 100
i.e. when n=1 we have:
Also,
Also,
Hence, the recursive formula is:
The linear function is given by:
It is given that the rate of change of the linear function is equal to the average rate of change of function f on the interval [-1, 1].
The slope(m) or average rate of change of the linear function will be:
and the linear function pass through (1,-2)
We know that the equation of a line with given slope m and passing through point (a,b) is given by:
Here (a,b)=(1,-2)
and
Hence, the equation of linear function is:
You would multiply the 3 to every term giving you,
12 + 6
x + 15
(Note that when multiplying a squared root number, you add the the exponents together. Also a term/number without an exponent is understood to have a 1 as the exponent, it is just not written)