Question

Complete the missing parts of the

table for the following function.
y = ( 1/1 ) x
x -2 -1
-2 -1
[?] 4
0 1
[] 1
4
2
1
16
3
1

Answer 1

`\begin{array}c c c c c c\sf{x} & \sf{-2} & \sf{-1} & \sf{0} & \sf{1} & \sf{2} & \sf{3}\\\cline{1-7} \sf{y} & \sf{16} & \sf{4} & \sf{1} & \sf{(1)/(4)} & \overline{\sf{(1)/(16)}} & \sf{(1)/(64)}\end{array}`

Explanation:

Given function:

`\sf y=\left((1)/(4)\right)^x`

In order to find the missing parts of the table, substitute the x-values into the given function to find the y-values.

When x = -2:

`\sf \\\implies y=\left((1)/(4)\right)^(-2)\ \Bigg( \textsf{Apply the rule:} \left((1)/(a)\right)^(-n)=a^n \Bigg)\\\\\implies y=4^2\\\\\implies y=\boxed{\sf16}`

When x = 0:

`\sf \\\implies y=\left((1)/(4)\right)^0\ \Bigg( \textsf{Apply the rule: }x^0=1 \Bigg)\\\\\implies y=\boxed{\sf1}`

When x = 3:

`\sf \\\implies y=\left((1)/(4)\right)^3\ \Bigg( \textsf{Apply the rule:} \left((x)/(y)\right)^(n)=(x^n)/(y^n) \Bigg)\\\\\implies y=(1^3)/(4^3)\\\\\implies y=\sf \frac{1}{\boxed{64}}}`