Final answer:
The transformation from the graph of f(x) to r(x) results in r(x) being a vertical stretch by a factor of 4 of f(x), making the graph of r(x) steeper with an unchanged y-intercept.
Step-by-step explanation:
To describe the transformation from the graph of function f to function r, where f(x) = -1/4x - 2 and r(x) = 4f(x), we first need to recognize what happens when we multiply the function f by 4. The function r(x) will also be a linear function because it's a scalar multiple of another linear function. The effect of multiplying by 4 is to stretch the graph of f vertically by a factor of 4, making the slope of r(x) four times steeper than that of f(x). The new slope for r(x) is -1 because 4 × (-1/4) equals -1. However, the y-intercept remains the same because multiplying by 4 also affects the constant -2, making it -8. Thus, the graph of r(x) will be steeper with the same y-intercept as f(x).