Question

The graph of f(x) is shown below.

For each point (a,b) on the graph of y = f(x), the point ( 3a - 1, b/2) is plotted to form the graph of another function y = g(x). For example, (0,2) lies on the graph of y = f(x), so (3 * 0 - 1, 2/2) = (-1,1) lies on the graph of y = g(x).
(a) Plot the graph of y = g(x). Include the diagram in your solution.
(b) Express g(x) in terms of f(x).
(c) Describe the transformations that you would apply to the graph of y = f(x) to obtain the graph of y = g(x). For example, one transformation might be to stretch the graph horizontally by a factor of 5

Answer 1

(a) I have attached the graph.

(b) The function g(x) is given by g(x) = f(2x + 2)/3. You can work this out algebraically. You can also work this out by using the graph of the function.

(c) We can obtain the graph of y = g(x) from the graph of y = f(x) through the following transformations:

* stretch horizontally by a factor of 2

* stretch vertically by a factor of 3

* shift downwards by 2 units