The problem asks us to graph the exponential function $y = 0.5 \cdot 2^x$. We can achieve this by selecting several $x$ values, calculating corresponding $y$ values, and plotting these points on the provided coordinate plane.

1. Problem Description

The problem asks us to graph the exponential function $y = 0.5 \cdot 2^x$. We can achieve this by selecting several $x$ values, calculating corresponding $y$ values, and plotting these points on the provided coordinate plane.

2. Solution Steps

First, let's create a table of values for the function $y = 0.5 \cdot 2^x$.

We will select some integer values for $x$ between -3 and

3.

For $x = -3$:

$y = 0.5 \cdot 2^{-3} = 0.5 \cdot \frac{1}{8} = \frac{1}{2} \cdot \frac{1}{8} = \frac{1}{16} = 0.0625$

For $x = -2$:

$y = 0.5 \cdot 2^{-2} = 0.5 \cdot \frac{1}{4} = \frac{1}{2} \cdot \frac{1}{4} = \frac{1}{8} = 0.125$

For $x = -1$:

$y = 0.5 \cdot 2^{-1} = 0.5 \cdot \frac{1}{2} = \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4} = 0.25$

For $x = 0$:

$y = 0.5 \cdot 2^0 = 0.5 \cdot 1 = 0.5$

For $x = 1$:

$y = 0.5 \cdot 2^1 = 0.5 \cdot 2 = 1$

For $x = 2$:

$y = 0.5 \cdot 2^2 = 0.5 \cdot 4 = 2$

For $x = 3$:

$y = 0.5 \cdot 2^3 = 0.5 \cdot 8 = 4$

Here is a table summarizing the values:

x | y

---|---

-3 | 0.0625

-2 | 0.125

-1 | 0.25

0 | 0.5

1 | 1

2 | 2

3 | 4

Now, we can plot these points on the coordinate plane and connect them to sketch the graph of the function.

3. Final Answer

The graph of $y = 0.5 \cdot 2^x$ is an exponential curve passing through the points (-3, 0.0625), (-2, 0.125), (-1, 0.25), (0, 0.5), (1, 1), (2, 2), and (3, 4).

(Note: I cannot physically plot the graph, but the description above tells you how to plot it.)