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Function Composition Naming - Name (First/Second) to Function

Level 1

This math topic focuses on identifying parts of composite functions, specifically distinguishing which function is first and which is second in an expression. Each question presents a composite function using function notation (e.g., \( y(b(x)) \)), and students must determine whether a specified function is the first or second in the composition. The exercise aims to develop understanding of function composition, an essential concept within the broader unit on functions, their composition, and inversion.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Function Composition Naming - Name (First/Second) to Function Worksheet

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Function Composition Naming - Name (First/Second) to Function
1
A LaTex expression showing \text{given }y(b(x))\\\\\text{second function is?}
What part of this composite function is the second function?
a A LaTex expression showing b(x)
b A LaTex expression showing y(x)
2
A LaTex expression showing \text{given }c(d(x))\\\\\text{second function is?}
What part of this composite function is the second function?
a A LaTex expression showing d(x)
b A LaTex expression showing c(x)
3
A LaTex expression showing \text{given }d(p(x))\\\\\text{first function is?}
What part of this composite function is the first function?
a A LaTex expression showing p(x)
b A LaTex expression showing d(x)
4
A LaTex expression showing \text{given }m(d(x))\\\\\text{first function is?}
What part of this composite function is the first function?
a A LaTex expression showing m(x)
b A LaTex expression showing d(x)
5
A LaTex expression showing \text{given }r(n(x))\\\\\text{second function is?}
What part of this composite function is the second function?
a A LaTex expression showing n(x)
b A LaTex expression showing r(x)
6
A LaTex expression showing \text{given }d(z(x))\\\\\text{second function is?}
What part of this composite function is the second function?
a A LaTex expression showing z(x)
b A LaTex expression showing d(x)
7
A LaTex expression showing \text{given }b(n(x))\\\\\text{second function is?}
What part of this composite function is the second function?
a A LaTex expression showing b(x)
b A LaTex expression showing n(x)
8
A LaTex expression showing \text{given }d(r(x))\\\\\text{second function is?}
What part of this composite function is the second function?
a A LaTex expression showing d(x)
b A LaTex expression showing r(x)