Function Composition to Domain - Root of Linear to Number Line (Level 1)

Function Composition to Domain - Root of Linear to Number Line

Level 1

This math topic centers around understanding and identifying the domain of a composite function involving linear and square root operations. Students are presented with multiple problems asking them to determine the correct domain of the function $ f(g(x)) $, where $ f(x) $ typically represents taking the square root of $ x $, and $ g(x) $ is a linear function. They must choose the correct domain displayed on number lines. It provides an introduction to function composition and the impact of function operations on domains, focusing on linear and square root functions.

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

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Function Composition to Domain - Root of Linear to Number Line Worksheet

Function Composition to Domain - Root of Linear to Number Line

$A LaTex expression showing \begin{align*}f(x)&=square root of x\\\\g(x)&=1x-3\\\\f(g(x)) &\rightarrow \text{Domain}?\end{align*}\\$

Which number line shows the domain of this function composition?

An svg image showing a possible answer to this math problem

$A LaTex expression showing \begin{align*}f(x)&=square root of x\\\\g(x)&=-1x+4\\\\f(g(x)) &\rightarrow \text{Domain}?\end{align*}\\$

Which number line shows the domain of this function composition?

$A LaTex expression showing \begin{align*}f(x)&=square root of x\\\\g(x)&=-1x+5\\\\f(g(x)) &\rightarrow \text{Domain}?\end{align*}\\$

Which number line shows the domain of this function composition?

$A LaTex expression showing \begin{align*}f(x)&=square root of x\\\\g(x)&=1x+5\\\\f(g(x)) &\rightarrow \text{Domain}?\end{align*}\\$

Which number line shows the domain of this function composition?

$A LaTex expression showing \begin{align*}f(x)&=square root of x\\\\g(x)&=-1x-3\\\\f(g(x)) &\rightarrow \text{Domain}?\end{align*}\\$

Which number line shows the domain of this function composition?

$A LaTex expression showing \begin{align*}f(x)&=square root of x\\\\g(x)&=1x-0\\\\f(g(x)) &\rightarrow \text{Domain}?\end{align*}\\$

Which number line shows the domain of this function composition?

$A LaTex expression showing \begin{align*}f(x)&=square root of x\\\\g(x)&=1x+1\\\\f(g(x)) &\rightarrow \text{Domain}?\end{align*}\\$

Which number line shows the domain of this function composition?

$A LaTex expression showing \begin{align*}f(x)&=square root of x\\\\g(x)&=1x-1\\\\f(g(x)) &\rightarrow \text{Domain}?\end{align*}\\$

Which number line shows the domain of this function composition?