Question

write a rule for the following function
x -1,0,1,2
y 3,1,1/3,1/9

Answer 1

1. Realise that y are all powers of 3
2. Realise that y and x are going the reverse direction, so the index must contain -x

Answer 2

Notice that \(\begin{matrix}x&-1&0&1&2\\\mbox{index of y}&1&0&-1&-2\end{matrix}\)

Answer 3

And notice that \(\begin{matrix}x&-1&0&1&2\\-x&1&0&-1&-2\end{matrix}\)

Answer 4

\[\Large\begin{array}{c|c|c|c|c}x&&-1&0&1&2\\\hline-x&&1&0&-1&-2\\\hline3^{-x}&&3&0&\frac13&\frac19\end{array}\]

Answer 5

sorry the second number of the row \(\large3^{-x}\) should be 1

Answer 6

okay i think i understand now thank you very much

Answer 7

no problem :)