Suppose the graph of f is given. Describe how the graphs of the following functions can be obtained from the graph of f.
y=3-f(x)
To obtain the graph of y=3-f(x) from the graph of f, you would reflect the graph of f(x) across the x-axis and then shift the entire graph upwards by 3 units.
This means each point on the original graph of f(x) will now be (x, 3 - y).
For example, if a point on the original graph was (2, 4), on the new graph it would be (2, 3-4) = (2, -1).
So the new graph will be the reflection of the original graph across the x-axis and shifted 3 units up.