This math topic focuses on the skill of function composition, particularly determining the domain of composite functions involving integer and linear transformations. The problems require understanding and calculating the domain after composition, followed by matching the obtained domain with its representation on a number line. This forms part of a larger discussion on functions, specifically their composition and inversion. Each question presents a composite function and asks the learner to identify the corresponding domain visualized on a number line. This skill is crucial for visualizing and understanding function behaviors and restrictions.

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Function Composition to Domain to Domain - Integer over Linear to Number Line Worksheet

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Function Composition to Domain to Domain - Integer over Linear to Number Line
1
A LaTex expression showing \begin{align*}f(x)&=4 over x \\\\g(x)&=1x+3\\\\f(g(x)) &\rightarrow \text{Domain}?\end{align*}\\
Which number line shows the domain of this function composition?
a An svg image showing a possible answer to this math problem
b An svg image showing a possible answer to this math problem
2
A LaTex expression showing \begin{align*}f(x)&=-4 over x \\\\g(x)&=1x+4\\\\f(g(x)) &\rightarrow \text{Domain}?\end{align*}\\
Which number line shows the domain of this function composition?
a An svg image showing a possible answer to this math problem
b An svg image showing a possible answer to this math problem
3
A LaTex expression showing \begin{align*}f(x)&=-4 over x \\\\g(x)&=1x-2\\\\f(g(x)) &\rightarrow \text{Domain}?\end{align*}\\
Which number line shows the domain of this function composition?
a An svg image showing a possible answer to this math problem
b An svg image showing a possible answer to this math problem
4
A LaTex expression showing \begin{align*}f(x)&=-1 over x \\\\g(x)&=1x+1\\\\f(g(x)) &\rightarrow \text{Domain}?\end{align*}\\
Which number line shows the domain of this function composition?
a An svg image showing a possible answer to this math problem
b An svg image showing a possible answer to this math problem
5
A LaTex expression showing \begin{align*}f(x)&=-5 over x \\\\g(x)&=1x-5\\\\f(g(x)) &\rightarrow \text{Domain}?\end{align*}\\
Which number line shows the domain of this function composition?
a An svg image showing a possible answer to this math problem
b An svg image showing a possible answer to this math problem
6
A LaTex expression showing \begin{align*}f(x)&=5 over x \\\\g(x)&=1x+1\\\\f(g(x)) &\rightarrow \text{Domain}?\end{align*}\\
Which number line shows the domain of this function composition?
a An svg image showing a possible answer to this math problem
b An svg image showing a possible answer to this math problem
7
A LaTex expression showing \begin{align*}f(x)&=-1 over x \\\\g(x)&=-1x+4\\\\f(g(x)) &\rightarrow \text{Domain}?\end{align*}\\
Which number line shows the domain of this function composition?
a An svg image showing a possible answer to this math problem
b An svg image showing a possible answer to this math problem
8
A LaTex expression showing \begin{align*}f(x)&=-3 over x \\\\g(x)&=-1x-0\\\\f(g(x)) &\rightarrow \text{Domain}?\end{align*}\\
Which number line shows the domain of this function composition?
a An svg image showing a possible answer to this math problem
b An svg image showing a possible answer to this math problem