Fluency exercise

## Problem

Match up each function with its domain and range. They form a set of domino cards that can be arranged in a sequence.

To turn the sequence into a closed loop, you will need to complete the cards with missing information. A separate sheet containing just those cards is available here.

 $f(x)=x^2+1$ domain: $x\neq-1$ range: $f(x)\neq0$
 $f(x)=|x|$ domain: $x\in \mathbb{R}$ range: $f(x)\ge1$
 $f(x)=\sqrt[3]{x}$ domain: $x\in \mathbb{R}$ range: $0\!<\!f(x)\!\le\!1$
 $f(x)=\sqrt{x}$ domain: $x\in \mathbb{R}$ range: $f(x)\ge-1$
 $f(x)=\frac{1}{x}$ domain: $x\neq0$ range: $f(x)\ne-1$
 $f(x)=x+\frac{1}{x}$ domain: $x\neq-1$, $x\neq1$ range: $f(x)\le-1$ or $f(x)>0$
 $f(x)=\frac{1}{x^2}$ domain: $x\in \mathbb{R}$ range: $f(x)\ge0$
 $f(x)=\frac{1}{x^2+1}$ domain: $x\ge0$ range: $f(x)\ge0$
 $f(x)=\frac{1}{x^2-1}$ domain: $x>0$ range: $f(x)>0$
 $f(x)=\frac{1}{1+x}$ domain: $x\ge0$ range: $f(x)\le\frac{2}{3}$
 $f(x)=\frac{1}{\sqrt{x}}$ domain: $x\in \mathbb{R}$ range: $f(x)\in \mathbb{R}$
 $f(x)=\sqrt{3x}(1-x)$ domain: $x\neq0$ range: $f(x)\neq0$
 $f(x)=\frac{1}{x}-1$ domain: range:
 $f(x)=\qquad\qquad$ domain: range: