Question

Explain how the sequence 10.6, 11.8 and 13 is a function even though there are multiple rules that can represent it

Answer 1

The sequence is a function because each rule produces one output for each input.

Answer 2

Answer with explanation:

The given sequence is , 10.6, 11.8 and 13.

If you represent this through three terms of the sequence or function ,it can be written as:

 (1, 10.6), (2, 11.8), (3,13).

This is a linear function or Arithmetic Sequence because difference between two consecutive terms is same.

→11.8 - 10.6=13-11.8=1.2

Slope between two points

       $=\frac{11.8-10.6}{2-1}\\\\=\frac{13-11.8}{3-2}\\\\=1.2$

Equation of Line can be Written with the help of following formula

     $\frac{y-y_{1}}{x-x_{1}}=m\\\\ \frac{y-10.6}{x-1}=1.2\\\\y-10.6=1.2 \times (x-1)\\\\y-10.6=1.2 x -1.2\\\\12 x -10y+106-12=0\\\\12 x - 10 y+94=0\\\\6 x - 5 y+47=0$

So, the following Sequence , 10.6, 11.8 and 13 represents a Linear Function.

The function is: 6 x -5 y +47=0