Source: Stewart, James. Calculus: Early Transcendentals (6 edn 2007).
[p. 50 Top:] To understand how the expression for a function relates to its graph, it’s helpful to graph a family of functions, that is, a collection of functions whose equations are related. In the next example we graph members of a family of cubic polynomials.
[p. 391 Middle:] You should distinguish carefully between definite and indefinite integrals. A definite integral $\int^b_a f(x) \,dx$ is a number, whereas an indefinite integral $\int f(x) \,dx$ is a function (or family [format mine] of functions).
Of functions: how does 'family' differ from 'set'?
Why did James Stewart write 'family' instead of 'set'?
I read this that feels too advanced for univariate calculus.