Vertical Translations.
Compared with the graph of \(y = f (x)\text{,}\)
- The graph of \(~~y=f(x)+k,~~(k\gt 0)~~\) is shifted upward \(k\) units.
- The graph of \(~~y=f(x)-k,~~(k\gt 0~~)\) is shifted downward \(k\) units.
\(x\) | \(-2\) | \(-1\) | \(~0~\) | \(~~1~~\) | \(~2~\) |
\(y=x^2\) | \(4\) | \(1\) | \(0\) | \(1\) | \(4\) |
\(f(x)=x^2+4\) | \(8\) | \(5\) | \(4\) | \(5\) | \(8\) |
\(x\) | \(-2\) | \(-1\) | \(0\) | \(1\) | \(2\) |
\(y=x^2\) | \(4\) | \(1\) | \(0\) | \(1\) | \(4\) |
\(g(x)=x^2-4\) | \(0\) | \(-3\) | \(-4\) | \(-3\) | \(0\) |
\(x\) | \(-2\) | \(-1\) | \(0\) | \(1\) | \(2\) |
\(y=\abs{x}\) | \(2\) | \(1\) | \(0\) | \(1\) | \(2\) |
\(g(x)=\abs{x}+3\) | \(5\) | \(4\) | \(3\) | \(4\) | \(5\) |
\(x\) | \(-2\) | \(-1\) | \(\dfrac{1}{2}\) | \(1\) | \(2\) |
\(y=\dfrac{1}{x}\) | \(\dfrac{-1}{2}\) | \(-1\) | \(2\) | \(1\) | \(\dfrac{1}{2}\) |
\(h(x)=\dfrac{1}{x}-2\) | \(\dfrac{-5}{2}\) | \(-3\) | \(0\) | \(-1\) | \(\dfrac{-3}{2}\) |
\(x\) | \(-1\) | \(0\) | \(1\) | \(2\) | \(3\) |
\(y=\sqrt{x}\) | undefined | \(0\) | \(1\) | \(1.414\) | \(1.732\) |
\(y=\sqrt{x+1}\) | \(0\) | \(1\) | \(1.414\) | \(1.732\) | \(2\) |
\(x\) | \(-1\) | \(0\) | \(1\) | \(2\) | \(3\) | \(4\) |
\(y=\dfrac{1}{x}\) | \(1\) | undefined | \(1\) | \(\dfrac{1}{4}\) | \(\dfrac{1}{9}\) | \(\dfrac{1}{16}\) |
\(y=\dfrac{1}{(x-3)^2}\) | \(\dfrac{1}{16}\) | \(\dfrac{1}{9}\) | \(\dfrac{1}{4}\) | \(1\) | undefined | \(1\) |
\(x\) | \(y=x^2\) | \(f(x)=2x^2\) |
\(-2\) | \(4\) | \(8\) |
\(-1\) | \(1\) | \(2\) |
\(0\) | \(0\) | \(0\) |
\(1\) | \(1\) | \(2\) |
\(2\) | \(4\) | \(8\) |
\(x\) | \(y=x^2\) | \(g(x)=\frac{1}{2}x^2\) |
\(-2\) | \(4\) | \(2\) |
\(-1\) | \(1\) | \(\frac{1}{2}\) |
\(0\) | \(0\) | \(0\) |
\(1\) | \(1\) | \(\frac{1}{2}\) |
\(2\) | \(4\) | \(2\) |
\(x\) | \(y=x^2\) | \(h(x)=-x^2\) |
\(-2\) | \(4\) | \(-4\) |
\(-1\) | \(1\) | \(-1\) |
\(0\) | \(0\) | \(0\) |
\(1\) | \(1\) | \(-1\) |
\(2\) | \(4\) | \(-4\) |
\(x\) | \(~~1~~\) | \(~~2~~\) | \(~~3~~\) | \(~~4~~\) | \(~~5~~\) | \(~~6~~\) |
\(f(x)\) | \(8\) | \(6\) | \(4\) | \(2\) | \(0\) | \(2\) |
\(~~x~~\) | \(~~1~~\) | \(~~2~~\) | \(~~3~~\) | \(~~4~~\) | \(~~5~~\) | \(~~6~~\) |
\(y\) | \(10\) | \(8\) | \(6\) | \(4\) | \(2\) | \(4\) |
\(~~x~~\) | \(~~1~~\) | \(~~2~~\) | \(~~3~~\) | \(~~4~~\) | \(~~5~~\) | \(~~6~~\) |
\(y\) | \(4\) | \(2\) | \(0\) | \(-2\) | \(-4\) | \(-2\) |
\(~~x~~\) | \(~~1~~\) | \(~~2~~\) | \(~~3~~\) | \(~~4~~\) | \(~~5~~\) | \(~~6~~\) |
\(y\) | \(4\) | \(3\) | \(2\) | \(1\) | \(0\) | \(1\) |
\(~~x~~\) | \(~~1~~\) | \(~~2~~\) | \(~~3~~\) | \(~~4~~\) | \(~~5~~\) | \(~~6~~\) |
\(y\) | \(10\) | \(8\) | \(6\) | \(4\) | \(2\) | \(0\) |
\(x\) | \(~-3~\) | \(~-2~\) | \(~-1~\) | \(~~0~~\) | \(~~1~~\) | \(~~2~~\) |
\(f(x)\) | \(13\) | \(3\) | \(-3\) | \(-5\) | \(-3\) | \(3\) |
\(x\) | \(~-3~\) | \(~-2~\) | \(~-1~\) | \(~~0~~\) | \(~~1~~\) | \(~~2~~\) |
\(y\) | \(-26\) | \(-6\) | \(6\) | \(10\) | \(6\) | \(-6\) |
\(x\) | \(~-3~\) | \(~-2~\) | \(~-1~\) | \(~~0~~\) | \(~~1~~\) | \(~~2~~\) |
\(y\) | \(18\) | \(8\) | \(2\) | \(0\) | \(2\) | \(8\) |
\(x\) | \(~-3~\) | \(~-2~\) | \(~-1~\) | \(~~0~~\) | \(~~1~~\) | \(~~2~~\) |
\(y\) | \(-3\) | \(-5\) | \(-3\) | \(3\) | \(13\) | \(27\) |
\(x\) | \(~-3~\) | \(~-2~\) | \(~-1~\) | \(~~0~~\) | \(~~1~~\) | \(~~2~~\) |
\(y\) | \(2.6\) | \(0.6\) | \(-0.6\) | \(-1\) | \(-0.6\) | \(0.6\) |
\(x\) | \(~-2~\) | \(~-1~\) | \(~~0~~\) | \(~~1~~\) | \(~~2~~\) | \(~~3~~\) |
\(f(x)\) | \(-9\) | \(-8\) | \(-7\) | \(-6\) | \(1\) | \(20\) |
\(~~x~~\) | \(~-2~\) | \(~-1~\) | \(~~0~~\) | \(~~1~~\) | \(~~2~~\) | \(~~3~~\) |
\(y\) | \(-34\) | \(-9\) | \(-8\) | \(-7\) | \(-6\) | \(1\) |
\(~~x~~\) | \(~-2~\) | \(~-1~\) | \(~~0~~\) | \(~~1~~\) | \(~~2~~\) | \(~~3~~\) |
\(y\) | \(-4\) | \(21\) | \(22\) | \(23\) | \(24\) | \(31\) |
\(~~x~~\) | \(~-2~\) | \(~-1~\) | \(~~0~~\) | \(~~1~~\) | \(~~2~~\) | \(~~3~~\) |
\(y\) | \(18\) | \(16\) | \(14\) | \(12\) | \(-2\) | \(-40\) |
\(~~x~~\) | \(~-2~\) | \(~-1~\) | \(~~0~~\) | \(~~1~~\) | \(~~2~~\) | \(~~3~~\) |
\(y\) | \(8\) | \(6\) | \(4\) | \(2\) | \(-12\) | \(-50\) |
\(x\) | \(~~1~~\) | \(~~2~~\) | \(~~3~~\) | \(~~4~~\) | \(~~5~~\) | \(~~6~~\) |
\(f(x)\) | \(60\) | \(30\) | \(20\) | \(15\) | \(12\) | \(10\) |
\(x\) | \(~~1~~\) | \(~~2~~\) | \(~~3~~\) | \(~~4~~\) | \(~~5~~\) | \(~~6~~\) |
\(y\) | \(30\) | \(15\) | \(10\) | \(7.5\) | \(6\) | \(5\) |
\(x\) | \(~~1~~\) | \(~~2~~\) | \(~~3~~\) | \(~~4~~\) | \(~~5~~\) | \(~~6~~\) |
\(y\) | \(35\) | \(20\) | \(15\) | \(12.5\) | \(11\) | \(10\) |
\(x\) | \(~~1~~\) | \(~~2~~\) | \(~~3~~\) | \(~~4~~\) | \(~~5~~\) | \(~~6~~\) |
\(y\) | \(-12\) | \(-6\) | \(-4\) | \(-3\) | \(-2.4\) | \(-2\) |
\(x\) | \(~~1~~\) | \(~~2~~\) | \(~~3~~\) | \(~~4~~\) | \(~~5~~\) | \(~~6~~\) |
\(y\) | \(-10\) | \(-4\) | \(-2\) | \(-1\) | \(1.4\) | \(0\) |