Final answer:
The graph of a function can be formed from its parent function via translation, reflection, stretching, compressing, rotation, and dilation. Changing the slope or y-intercept of a linear equation results in rotational or vertical translation of its graph, respectively.
Step-by-step explanation:
To produce the graph of a function from its parent function, the transformations that should be applied include translation and reflection. Translation moves the graph vertically or horizontally without changing its shape or orientation. Reflection flips the graph over a given axis. Other transformations include stretching and compressing, which change the graph's size vertically or horizontally, respectively. Additionally, rotating the graph changes its orientation without altering its shape, and dilation alters the size of the graph both horizontally and vertically.
Equations of a line, such as y = mx + b, where 'm' represents the slope and 'b' is the y-intercept, can be manipulated by changing these parameters. Increasing the slope 'm' will cause the line to rotate counter-clockwise around the y-intercept, whereas changing the y-intercept 'b' will translate the line up or down the graph. Understanding how to read and manipulate a graph is essential when working with linear functions and their transformations.