consider the function y = 3x². how do the y - values of this function grow? by adding 3 by adding 9 by…

consider the function y = 3x². how do the y - values of this function grow? by adding 3 by adding 9 by multiplying the previous y - value by 3 by adding 3, then 9, then 15, ... done

consider the function y = 3x². how do the y - values of this function grow? by adding 3 by adding 9 by multiplying the previous y - value by 3 by adding 3, then 9, then 15, ... done

Answer

Explanation:

Step1: Let's take two consecutive integer - valued inputs

Let (x = n) and (x=n + 1). When (x=n), (y_1=3n^{2}). When (x=n + 1), (y_2=3(n + 1)^{2}=3(n^{2}+2n + 1)=3n^{2}+6n+3).

Step2: Find the difference between (y_2) and (y_1)

(y_2−y_1=(3n^{2}+6n + 3)-3n^{2}=6n + 3). When (n = 1), (y_1=3\times1^{2}=3), (y_2=3\times2^{2}=12), and (y_2 - y_1=9). When (n = 2), (y_1=3\times2^{2}=12), (y_2=3\times3^{2}=27), and (y_2 - y_1=15). The differences are (9,15,\cdots) which follow the pattern of adding (3,9,15,\cdots) to the previous (y) - value.

Answer:

by adding 3, then 9, then 15, ...