Final answer:
The function notation representing a linear relationship between two sets in the form y = mx + b is f(x) = 2x, which is option B. Options A, C, and D do not represent linear equations.
Step-by-step explanation:
The question is asking which function notation best represents the linear relationship between two sets of data. The typical form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept. Since the linear equations we use in this course are expressed in this form, we can look at the provided options to determine the correct answer.
Option A, f(x) = y, does not represent a specific relationship; it is simply stating that f(x) is another name for y. Option B, f(x) = 2x, represents a linear relationship with a slope of 2 and no y-intercept, which fits the form y = mx + b with b being zero. Option C, f(x) = x^2, represents a quadratic relationship, which is indicated by the squared term and is not linear. Option D, f(x) = √x, represents an inverse relationship, which is also non-linear.
Therefore, the function notation that best represents a linear relationship between the sets, according to the form y = mx + b, would be B. f(x) = 2x.