Given the graph of `y=f(x)`.

Draw the graphs of the followin.
(a) `y=f(1-x)` (b) `y=-2f(x)`
(c) `y=f(2x)` (d) `y=1-f(x)`

Explanation

(a) `y=f(1-x)`
For the graph of `y=f(x)`, flip the graph of `y=f(x)` over the y-axis.

For the graphs of `y=f(1-x)`, shift the above graph '1' units to the right horizontally.

(c) `y=f(2x)`
For the graph of `y=f(2x)`, compress the graph of `y=f(x)'2'` times horizontally.

(c) `y=-2f(x)`
For the graph of `y=2f(x)`, stretch the graph of `y=f(x)'2'` times vertically.

For the graph of `y=-2f(x)`, flip the above graph over the x-axis.

(d) `y=1-f(x)`
For the graph of `y=-f(x)`, flip the graph of `y=f(x)` over the x-axis.

For the graph of `y=1-f(x)`, shift the above graph by '1' unit vertically.