Question

Suppose you are given the graph of y = f (x) . Explain how to obtain the graphs of

a. y = f (x / 2)
b. y = f (x - 2)
c. y = f (2 x - 1)

Answer 1

Suggest you make yourself a list of transformations and their associated rules. The ones you're concerned with here are
.. f(x) ⇒ f(kx) . . . . . . horizontal compression by a factor of k
.. f(x) ⇒ f(x -k) . . . . . right shift by k units

a) Each point (x, y) gets moved to (2x, y). The graph is expanded horizontally by a factor of 2.

b) Each point (x, y) gets moved to (x+2, y). The graph is translated horizontally 2 units to the right.

c) Each point (x, y) gets moved to ((x +1)/2, y). The graph is translated horizontally 1 unit to the right, then compressed horizontally by a factor of 2.