The problem asks us to plot the graph of the exponential function $y = 0.5 \cdot 2^x$ on the given coordinate plane.

1. Problem Description

The problem asks us to plot the graph of the exponential function $y = 0.5 \cdot 2^x$ on the given coordinate plane.

2. Solution Steps

To plot the graph of $y = 0.5 \cdot 2^x$, we can evaluate the function for several values of $x$ and then plot the resulting points.

If $x = -2$, then $y = 0.5 \cdot 2^{-2} = 0.5 \cdot \frac{1}{4} = \frac{1}{2} \cdot \frac{1}{4} = \frac{1}{8} = 0.125$. The point is $(-2, 0.125)$.

If $x = -1$, then $y = 0.5 \cdot 2^{-1} = 0.5 \cdot \frac{1}{2} = \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4} = 0.25$. The point is $(-1, 0.25)$.

If $x = 0$, then $y = 0.5 \cdot 2^0 = 0.5 \cdot 1 = 0.5$. The point is $(0, 0.5)$.

If $x = 1$, then $y = 0.5 \cdot 2^1 = 0.5 \cdot 2 = 1$. The point is $(1, 1)$.

If $x = 2$, then $y = 0.5 \cdot 2^2 = 0.5 \cdot 4 = 2$. The point is $(2, 2)$.

If $x = 3$, then $y = 0.5 \cdot 2^3 = 0.5 \cdot 8 = 4$. The point is $(3, 4)$.

If $x = 4$, then $y = 0.5 \cdot 2^4 = 0.5 \cdot 16 = 8$. The point is $(4, 8)$.

Now, we can plot these points on the coordinate plane and draw a smooth curve through them.

3. Final Answer

The graph is the curve passing through the points $(-2, 0.125)$, $(-1, 0.25)$, $(0, 0.5)$, $(1, 1)$, $(2, 2)$, $(3, 4)$, and $(4, 8)$.

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