Final answer:
The transformed function based on the parent function f(x) = 3x that has been moved right by 4 units and down 2 units is g(x) = 3(x - 4) - 2.
Step-by-step explanation:
The student is asking about a transformation of a linear function. The parent function is f(x) = 3x. The student describes a shift over the x-axis, a movement to the right by 4 units, and a downward shift by 2 units. The transformation over the x-axis doesn't change the function since it's a linear function and not a reflection.
To move the function right by 4 units, we replace x with (x - 4). To shift it down by 2 units, we subtract 2 from the entire function. Therefore, the new function after the described transformations is g(x) = 3(x - 4) - 2.
Functions can take many forms, including linear, quadratic, trigonometric, exponential, logarithmic, and more. They're fundamental in mathematics and have applications across various fields like physics, engineering, economics, and computer science.
They help describe relationships between quantities and are essential in modeling real-world phenomena.