Final answer:
The transformation g(x) = 3x - 4 involves a vertical scaling by a factor of 3, making the graph steeper, and a downward translation of 4 units along the y-axis.
Step-by-step explanation:
The transformation of the function g(x) = 3x - 4 involves two main operations on the input variable x: scaling and translation. The coefficient 3 in front of x indicates a scaling transformation. This means that the graph of g(x) is stretched vertically by a factor of 3 compared to the graph of the basic function f(x) = x. The subtraction of 4 from 3x represents a translation transformation. Specifically, it translates the graph of the function 4 units down along the y-axis.
Scaling Transformation
The scaling effect due to the coefficient of 3 means that for every 1 unit increase in the input x, the output g(x) increases by 3 units instead of just 1. If we compare g(x) to the identity function f(x) = x, we would notice that the slope of g(x) is 3 times steeper.
Translation Transformation
The translation of 4 units down is because every output value from the function 3x is reduced by 4 units. This results in the graph being shifted downward, such that, for example, the point (0, 0) on the graph of f(x) = x would be moved to (0, -4) on the graph of g(x).