Reflection across the x-axis vertical compression by 1/2 translated 2 units left translated 3 units up equation
To reflect a graph across the x-axis, we negate the y-coordinate.
To vertically compress a graph by 1/2, we multiply the y-coordinate by 1/2.
To translate a graph 2 units to the left, we subtract 2 from the x-coordinate.
To translate a graph 3 units up, we add 3 to the y-coordinate.
Let's say the equation of the original graph is y = f(x).
After the reflection across the x-axis, the equation becomes y = -f(x).
After the vertical compression by 1/2, the equation becomes y = -(1/2)f(x).
After the translation 2 units to the left, the equation becomes y = -(1/2)f(x + 2).
After the translation 3 units up, the equation becomes y = -(1/2)f(x + 2) + 3.