The graph of y = f(x) is shown below.
For each point (a,b) that is on the graph of y = f(x), the point ((a - 7)/2, (3b + 1)/4) is plotted, forming the graph of another function y = g(x). As an example, the point (0,2) lies on the graph of y = f(x), so the point lies on the graph of y = g(x).
(a) Plot the graph of y = g(x). Include the diagram as part of your solution.
(b) Express g(x) in terms of f(x)
(c) Describe the transformations that can be applied to the graph of y = f(x) to obtain the graph of y = g(x). For example, one transformation could be to stretch the graph vertically by a factor of 4.
Answer:
(a) The graph of y = g(x) is shown below:
(b) g(x) = (3f((x + 7)/2) + 1)/4
(c) The graph of y = g(x) is obtained by shifting the graph of y = f(x) 7 units to the left, stretching it vertically by a factor of 3, and shifting it 1 unit up.