Any suggestions on how to explain function composition in algebra?

Asked by LostInParadise (31924

) November 6th, 2016

I do some online tutoring and I have found that some students have a hard time with the idea of composing two functions. For example, if f(x)=3x+2 and g(x)=x+1, then f(g(x)) is 3(x+1)+2.

I tried the following, but it did not seem to work. f(g(x)) = 3(g(x)) + 1 = 3(x+1) + 2. Any other ideas? I was thinking that if students were taught to program a language like Python then the two functions could be translated into two software functions and it might be clearer.

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4 Answers

I think there is an error here where you write… = 3(g(x)) + 1 = ... that + 1 there should be a + 2, right?

Maybe try writing the functions in different colors or fonts to emphasize how the one plugs right into the other.

Zissou (3374

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My precalc teacher did this great as part of basic function substitution. Basically:

F(x) = x+3
F(t) = ? (Someone raises their hand, substitutes in t+3.
F(7) = 7+3 = 10.
F(☺️) = ☺️ + 3 (good absurd example showing you to just blindly substitute what’s in the parens).
F(x+2) = x +2 +3 = x + 5
G(x) = x + 2
F(G(x)) = x + 2 + 3 = x + 5

Mariah (25883

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I will give that a try next time.

LostInParadise (31924

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When I try explaining it, I write out the original function and then circle with red the x’s. Then, I write the function composition underneath and circle the g(x)‘s, to show that you’re putting it into the function in the same way.
I wish we could show them rotations and reflections. That might help them understand it. Or maybe not.

dxs (15160

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