Question

Complete the table for the following functiony=(1/3)^x*imageGraph the function and describe what the graph looks like.A. Increases in Quadrant Ib. Increases from left to rightc. Decreases from left to rightd. Decreases in Quadrant III

Answer 1

Given:-

`y=((1)/(3))^x`

To graph the image.

So now we find the values of y when the value of x is -3,-2,-1,0,1,2,3.

When x is -3. we get,

`\begin{gathered} y=((1)/(3))^(-3) \\ y=(3)^3 \\ y=27 \end{gathered}`

So the required value is 27.

when x is -2. we get,

`\begin{gathered} y=((1)/(3))^(-2) \\ y=(3)^2 \\ y=9 \end{gathered}`

So the required value is 9.

When x is -1. we get,

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

So the required value is 3.

When x is 0. we get,

`\begin{gathered} y=((1)/(3))^0 \\ y=0 \end{gathered}`

So the required value is 0.

When x is 1. we get,

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

So the required value is 1/3.

When x is 2. we get,

`\begin{gathered} y=((1)/(3))^2 \\ y=(1)/(9) \end{gathered}`

So the required value is 1/9.

When x is 3. we get,

`\begin{gathered} y=((1)/(3))^3 \\ y=(1)/(27) \end{gathered}`

So the required value is 1/27.

So the graph looks like,

This is the graph and it decreases from left to right.