Question

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

Answer 1

The given expression :

$y=(\frac{1}{2})^x$

For coordinates:

put x = 0 then :

$\begin{gathered} y=(\frac{1}{2})^0 \\ y=1 \end{gathered}$

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

Put x= 1 and simplify :

$\begin{gathered} y=(\frac{1}{2})^1 \\ y=\frac{1}{2} \\ y=0.5 \end{gathered}$

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

Put x = (-2) and simplify :

$\begin{gathered} y=(\frac{1}{2})^{-2} \\ y=\frac{1^{-2}}{2^{-2}} \\ y=\frac{2^2}{1^2} \\ y=2^2 \\ y=4 \end{gathered}$

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

Put x = (-3) and simplify :

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

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

Substitute x = (-1) and simplify :

$\begin{gathered} y=(\frac{1}{2})^x \\ y=(\frac{1}{2})^{-1} \\ y=\frac{1^{-1}}{2^{-1}} \\ y=\frac{2}{1} \\ y=2 \end{gathered}$

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

So, the coordinates are :

The graph is :