Final answer:
The graph of g(x) = 4x is a vertical stretch of the graph of f(x) = x by a factor of 4. This means each y-value is multiplied by 4, resulting in a steeper line on the graph.
Step-by-step explanation:
The transformation of the graph of f(x) = x that results in the graph of g(x) = 4x is called a stretch or dilation. When you multiply each y-value (or output) of the function f(x) by 4, you end up stretching the graph vertically by a factor of 4.
This means that for every x-value, the corresponding y-value on the graph of g(x) is 4 times greater than the y-value at the same x on the graph of f(x).
To visualize this, if you label the graph with f(x) and x, and scale the x and y axes with the maximum x and y values of f(x) = 10 and 0≤x≤20, respectively, you'll notice that the line y=x becomes a steeper line under the transformation to g(x) = 4x. An example point (2,2) on f(x) would become (2,8) on g(x).