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:-

$y=(\frac{1}{3})^x$

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,

$\begin{gathered} y=(\frac{1}{3})^{-3} \\ y=(3)^3 \\ y=27 \end{gathered}$

So the required value is 27.

when x is -2. we get,

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

So the required value is 9.

When x is -1. we get,

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

So the required value is 3.

When x is 0. we get,

$\begin{gathered} y=(\frac{1}{3})^0 \\ y=0 \end{gathered}$

So the required value is 0.

When x is 1. we get,

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

So the required value is 1/3.

When x is 2. we get,

$\begin{gathered} y=(\frac{1}{3})^2 \\ y=\frac{1}{9} \end{gathered}$

So the required value is 1/9.

When x is 3. we get,

$\begin{gathered} y=(\frac{1}{3})^3 \\ y=\frac{1}{27} \end{gathered}$

So the required value is 1/27.

So the graph looks like,

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