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I am not a mathematics teacher, I just want to know which function is more elementary and is more reasonable to be learnt first:

  • Constant function (f(x)=1)
  • Identity function (f(x)=x)

Thank you,

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    $\begingroup$ At what level are you teaching? The answer differs if you are introducing graphing to algebra 1 students or the concept of a function with function notation to precalculus students, for example. $\endgroup$
    – Opal E
    Oct 26, 2021 at 3:08
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    $\begingroup$ Are you the same user as matheducators.stackexchange.com/users/17917/chichorozov? $\endgroup$
    – J W
    Oct 26, 2021 at 6:26
  • $\begingroup$ @OpalE I don't teach, I want to understand what I should learn myself in the future first. $\endgroup$ Oct 26, 2021 at 9:50
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    $\begingroup$ If you want to decide/know which function you should learn first, does this mean that you are currently unfamiliar with $f(x) = 1$ and $f(x) = x$? Could you please clarify what your learning goals are? $\endgroup$
    – J W
    Oct 26, 2021 at 11:23
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    $\begingroup$ I do not understand the point of these questions. $\endgroup$
    – Sue VanHattum
    Oct 26, 2021 at 18:14

1 Answer 1

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In algebra 1, kids learn y =mx+b. Then, soon after and during same year m=0 or b=0 are special cases of the general. Not sure which of the subcases first between each other (doesn't matter much) and in any cases, they're learned as types of lines. (Of course the one other line they learn is x = k, which of course is not a function--is a relation--and is not a subset of y = mx +b.)

Given your previous question about real analysis and linear algebra content, I don't really get the question here. Seems so simple for someone so advanced. If it's not a troll (which it, Bayesian bet, probably is), then I'm confused what you're asking and how to help/engage.

(Stereotypically, in the US) you'll have algebra 1 in 9th, geometry in 10th, algebra2 in 11th and get function concept as part of 12th precalc. So in learning the function concept, you have some background of knowledge to use.

Bottom line is if you start working on the function CONCEPT, you're generally doing that after already having some exposure to equations, graphing, etc. so you have a baseline of experience to match against the function concept itself. And then you work on function concept (in/out machine, pairs of numbers, certain equations, graphically). In particular, understanding functions (no more than one y for an x) versus non-function relations. Like y=mx+b versus xsq+ysq=rsq. And the domain and range and blabla.

But when you learn the function CONCEPT, you're concentrating on the concept itself. You don't have to learn it fresh for different polynomials. You already have a background on those erquations from algebra 1 and 2. That hasn't disappeared. In fact, it's a resource to use. Maybe you'll learn a few functions that are new (like excluded end point, drawn with open circle, or like top half of a circle). But you don't have to relearn y=mx+b.

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