Question

Use a table of values with at least 5 values to graph the following function:

Answer 1

The given expression :

`y=((1)/(2))^x`

For coordinates:

put x = 0 then :

`\begin{gathered} y=((1)/(2))^0 \\ y=1 \end{gathered}`

Coordinate : (x, y) = (0, 1)

Put x= 1 and simplify :

`\begin{gathered} y=((1)/(2))^1 \\ y=(1)/(2) \\ y=0.5 \end{gathered}`

Coordinate : (x, y) = ( 1, 0.5)

Put x = (-2) and simplify :

`\begin{gathered} y=((1)/(2))^(-2) \\ y=(1^(-2))/(2^(-2)) \\ y=(2^2)/(1^2) \\ y=2^2 \\ y=4 \end{gathered}`

Coordinate : (x, y) = ( -2, 4)

Put x = (-3) and simplify :

`\begin{gathered} y=((1)/(2))^(-3) \\ y=(1^(-3))/(2^(-3)) \\ y=(2^3)/(1^3) \\ y=2^3 \\ y=8 \end{gathered}`

Coordinate : (x, y) = (-3, 8)

Substitute x = (-1) and simplify :

`\begin{gathered} y=((1)/(2))^x \\ y=((1)/(2))^(-1) \\ y=(1^(-1))/(2^(-1)) \\ y=(2)/(1) \\ y=2 \end{gathered}`

Coordinate : (x, y) = ( -1, 2)

So, the coordinates are :

The graph is :