Chapter SH, Problem 9.9.8EP

To determine

The graph of $y={\left(\frac{2}{3}\right)}^x$ is to be drawn.

Explanation of Solution

Given:

  $y={\left(\frac{2}{3}\right)}^x$

Graph:

  

Interpretation:

The given equation is:

  $y={\left(\frac{2}{3}\right)}^x$

At $x=2$

  $\begin{array}{l}y={\left(\frac{2}{3}\right)}^x\\ y={\left(\frac{2}{3}\right)}^2\\ y=0.44\end{array}$

At $x=1$

  $\begin{array}{l}y={\left(\frac{2}{3}\right)}^x\\ y={\left(\frac{2}{3}\right)}^1\\ y=0.66\end{array}$

At $x=0$

  $\begin{array}{l}y={\left(\frac{2}{3}\right)}^x\\ y={\left(\frac{2}{3}\right)}^0\\ y=1\end{array}$

At $x=-2$

  $\begin{array}{l}y={\left(\frac{2}{3}\right)}^x\\ y={\left(\frac{2}{3}\right)}^{-2}\\ y=2.25\end{array}$

At $x=-1$

  $\begin{array}{l}y={\left(\frac{2}{3}\right)}^x\\ y={\left(\frac{2}{3}\right)}^{-1}\\ y=1.5\end{array}$

So, the co-ordinates to draw eq. $y={\left(\frac{2}{3}\right)}^x$ are

  $\left(2,0.44\right),\left(1,0.66\right),\left(0,1\right),\left(-2,2.25\right),\left(-1,1.5\right)$