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 \(\left( 3a - 1, \frac{b}{2} \right)\)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 \((3 \cdot 0 - 1, 2/2) = (-1,1)\) lies on the graph of y = g(x).

(a) Plot the graph of y = g(x). Include the diagram 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.

PLEASE HELP!!! A thorough explanation would be appreciated since I am super confused and want to learn how to do this problem and other similar types of problems!!! Thank you so much!!!

Guest Nov 8, 2020