Chapter 7, Problem 18CT

To determine

To graph: the function $y=2\cdot {\left(\frac{1}{2}\right)}^x$ .

Explanation of Solution

Given:

The function is $y=2\cdot {\left(\frac{1}{2}\right)}^x$ .

Calculation:

Simplify the function as follows:

  $\begin{array}{c}y=2\cdot {\left(\frac{1}{2}\right)}^x\\ =2^1\cdot 2^{-x}\\ =2^{1-x}\end{array}$

Substitute values of x for the coordinates as follows:

For x = 1,

  $\begin{array}{c}y=2^{1-x}\\ =2^{1-1}\\ =1\end{array}$

Thus, the coordinate is (1, 1).

For x = -1,

  $\begin{array}{c}y=2^{1-x}\\ =2^{1-\left(-1\right)}\\ =4\end{array}$

Thus, the coordinate is (-1, 4).

For x = -2,

  $\begin{array}{c}y=2^{1-x}\\ =2^{1-\left(-2\right)}\\ =8\end{array}$

Thus, the coordinate is (-2, 8).

For x = 2,

  $\begin{array}{c}y=2^{1-x}\\ =2^{1-\left(2\right)}\\ =0.5\end{array}$

Thus, the coordinate is (2, 0.5).

Join the coordinates for the graph of given function as follows: