Use transformations to sketch the graph of the function. s(x)=1 + 0.5x

Step 1
${\displaystyle s\left(x\right)=1+{0.5}^x=1+{\left(\frac{1}{2}\right)}^X=1+2^{-x}}$
Remember that: When we reflect the graph of ${\displaystyle y=f\left(x\right)}$ in the y-axis, we get the graph for ${\displaystyle y=f(-x)}$
We will start the graph of the standard function ${\displaystyle y=2^x}$ (represented by blue dashed curve)
Reflect the graph of ${\displaystyle y=2^x}$ in the y-axis, to get the graph for ${\displaystyle y=2^{-x}}$ (represented by black solid curve)

Step 2
Remember that: When we shift the graph of ${\displaystyle y=f\left(x\right)}$ by k units upwards, we get the graph for ${\displaystyle y=f\left(x\right)+k}$
Shift the graph of ${\displaystyle y=2^{-x}}$ by 1 unit upwards, to get the graph for ${\displaystyle y=1+2^{-x}}$ (represented by red solid curve).
The graph for ${\displaystyle y=2^{-x}}$ is represented by black dashed curve.