Account for order in two vertical transformations

The Teacher emphasises y replaced by $y/2$, followed by y replaced by $y-1$. The source recommends scaling before translation for vertical changes.

Double output distances

$$\frac y2=f(x)\quad\Longrightarrow\quad y=2f(x)$$

Replace y by $y/2$ and solve for y.

Translate up one unit

$$y-1=2f(x)\quad\Longrightarrow\quad y=2f(x)+1$$

Apply the y-replacement to the current equation.

The Teacher emphasises y replaced by $y-1/2$, followed by y replaced by $y/2$. The later scaling also doubles the earlier translation.

Translate up one half

$$y-\frac12=f(x)\quad\Longrightarrow\quad y=f(x)+\frac12$$

Use the smaller translation before doubling.

Double all outputs

$$\frac y2=f(x)+\frac12\quad\Longrightarrow\quad y=2f(x)+1$$

The constant term is doubled as well.