Question

g is related to a parent function f (x) = sin (x) or f (x) = cos (x).

(a) Describe the sequence of transformations from f to g.

(b) Sketch the graph of g.

(c) Use function notation to write g in terms of f.

g (x) = sin (4x - π)

Answer 1

(a) The parent function is

Compare it to .

.

Amplitude = 1

Period

Find the left and right end points of one cycleby solving the equations and .

The graph og g is obtained by a horizontal shrink of four and one cycle of g corresponding to the interval .

Graph:

.

Answer 2

(b) Graph of .

Amplitude = 1

Period

Make a table to find the ordered pairs that satisfies equations. 

x		y	(x, y)

Draw the coordinate plane.

Plot the points found in the table and connect the curve.

Graph of .

.

(c) write the function g in terms of f.

.

Solution :

(c).