Step 1

$s\left(x\right)=1\text{}+\text{}{0.5}^{x}=1\text{}+\text{}{\left(\frac{1}{2}\right)}^{X}=1\text{}+\text{}{2}^{-x}$

Remember that: When we reflect the graph of $y=f\left(x\right)$ in the y-axis, we get the graph for $y=f(-x)$

We will start the graph of the standard function $y={2}^{x}$ (represented by blue dashed curve)

Reflect the graph of $y={2}^{x}$ in the y-axis, to get the graph for $y={2}^{-x}$ (represented by black solid curve)

Step 2

Remember that: When we shift the graph of $y=f\left(x\right)$ by k units upwards, we get the graph for $y=f\left(x\right)\text{}+\text{}k$

Shift the graph of $y={2}^{-x}$ by 1 unit upwards, to get the graph for $y=1\text{}+\text{}{2}^{-x}$ (represented by red solid curve).

The graph for $y={2}^{-x}$ is represented by black dashed curve.