Absolute Value.
The absolute value of \(x\) is defined by
\begin{equation*}
\abs{x} =
\begin{cases}
x \amp \text{if } x\ge 0\\
-x \amp \text{if } x\lt 0
\end{cases}
\end{equation*}
\(x\) | \(f(x)=x^2\) | \(g(x)=x^3\) |
\(-3\) | \(\) | \(\) |
\(-2\) | \(\) | \(\) |
\(-1\) | \(\) | \(\) |
\(-\frac{1}{2}\) | \(\) | \(\) |
\(0\) | \(\) | \(\) |
\(\frac{1}{2}\) | \(\) | \(\) |
\(1\) | \(\) | \(\) |
\(2\) | \(\) | \(\) |
\(3\) | \(\) | \(\) |
\(x\) | \(f(x)=\sqrt{x}\) |
\(0\) | \(\) |
\(\frac{1}{2}\) | \(\) |
\(1\) | \(\) |
\(2\) | \(\) |
\(3\) | \(\) |
\(4\) | \(\) |
\(5\) | \(\) |
\(7\) | \(\) |
\(9\) | \(\) |
\(x\) | \(g(x)=\sqrt[3]{x}\) |
\(-8\) | \(\) |
\(-4\) | \(\) |
\(-1\) | \(\) |
\(-\frac{1}{2}\) | \(\) |
\(0\) | \(\) |
\(\frac{1}{2}\) | \(\) |
\(1\) | \(\) |
\(4\) | \(\) |
\(8\) | \(\) |
\(x\) | \(f(x)=\dfrac{1}{x}\) | \(g(x)=\dfrac{1}{x^2}\) |
\(-4\) | \(\) | \(\) |
\(-3\) | \(\) | \(\) |
\(-2\) | \(\) | \(\) |
\(-1\) | \(\) | \(\) |
\(-\frac{1}{2}\) | \(\) | \(\) |
\(0\) | \(\) | \(\) |
\(\frac{1}{2}\) | \(\) | \(\) |
\(1\) | \(\) | \(\) |
\(2\) | \(\) | \(\) |
\(3\) | \(\) | \(\) |
\(4\) | \(\) | \(\) |
\(x\) | \(f(x)=\dfrac{1}{x}\) | \(g(x)=\dfrac{1}{x^2}\) |
\(-2\) | \(\) | \(\) |
\(-1\) | \(\) | \(\) |
\(-0.1\) | \(\) | \(\) |
\(-0.01\) | \(\) | \(\) |
\(-0.001\) | \(\) | \(\) |
\(x\) | \(f(x)=\dfrac{1}{x}\) | \(g(x)=\dfrac{1}{x^2}\) |
\(2\) | \(\) | \(\) |
\(1\) | \(\) | \(\) |
\(0.1\) | \(\) | \(\) |
\(0.01\) | \(\) | \(\) |
\(0.001\) | \(\) | \(\) |
\(x\) | \(f(x)=x\) | \(g(x)=\abs{x}\) |
\(-4\) | \(\) | \(\) |
\(-3\) | \(\) | \(\) |
\(-2\) | \(\) | \(\) |
\(-1\) | \(\) | \(\) |
\(-\frac{1}{2}\) | \(\) | \(\) |
\(0\) | \(\) | \(\) |
\(\frac{1}{2}\) | \(\) | \(\) |
\(1\) | \(\) | \(\) |
\(2\) | \(\) | \(\) |
\(3\) | \(\) | \(\) |
\(4\) | \(\) | \(\) |
\(\abs{a + b}\le\abs{a}+\abs{b} \) | Triangle inequality |
\(\abs{ab}=\abs{a}\abs{b} \) | Multiplicative property |
\(x\) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) |
\(y\) | \(-2\) | \(-1 \) | \(-\frac{1}{2} \) | \(0 \) | \(\frac{1}{2} \) | \(1 \) | \(2 \) |
\(x\) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) |
\(y\) | \(-2\) | \(-1 \) | \(-\frac{1}{2} \) | \(0 \) | \(\frac{1}{2} \) | \(1 \) | \(2 \) |
\(x\) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) |
\(y\) | \(-2\) | \(-1 \) | \(-\frac{1}{2} \) | \(0 \) | \(\frac{1}{2} \) | \(1 \) | \(2 \) |
\(x\) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) |
\(y\) | \(-2\) | \(-1 \) | \(-\frac{1}{2} \) | \(0 \) | \(\frac{1}{2} \) | \(1 \) | \(2 \) |
\(x\) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) |
\(y\) | \(-2\) | \(-1 \) | \(-\frac{1}{2} \) | \(0 \) | \(\frac{1}{2} \) | \(1 \) | \(2 \) |
\(x\) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) | \(\hphantom{000} \) |
\(y\) | \(-2\) | \(-1 \) | \(-\frac{1}{2} \) | \(0 \) | \(\frac{1}{2} \) | \(1 \) | \(2 \) |