Parent functions

Function Domain and
range		 Graph
Linear \(f(x)=x\) Domain \(\{x\in\mathbb{R}\}\)
Range \(\{y\in\mathbb{R}\}\)
Parent linear function
Quadratic \(f(x)=x^2\) Domain \(\{x\in\mathbb{R}\}\)
Range \(\{y\in\mathbb{R}\mid y\ge 0\}\)
Parent quadratic function
Absolute value \(f(x)=\lvert x\rvert\) Domain \(\{x\in\mathbb{R}\}\)
Range \(\{y\in\mathbb{R}\mid y\ge 0\}\)
Parent absolute value function
Square root \(f(x)=\sqrt{x}\) Domain \(\{x\in\mathbb{R}\mid x\ge 0\}\)
Range \(\{y\in\mathbb{R}\mid y\ge 0\}\)
Parent square root function
Reciprocal \(f(x)=\dfrac{1}{x}\) Domain \(\{x\in\mathbb{R}\mid x\neq0\}\)
Range \(\{y\in\mathbb{R}\mid y\neq 0\}\)
Parent reciprocal function
Exponential \(f(x)=b^x\)
\(b\gt 0;b\neq1\)		 Domain \(\{x\in\mathbb{R}\}\)
Range \(\{y\in\mathbb{R}\mid y\gt 0\}\)
Exponential function - base greater than unit
Sine \(f(x)=\sin x\) Domain \(\{x\in\mathbb{R}\}\)
Range \(\{y\in\mathbb{R}\mid -1\le y\le 1\}\)
Parent sine function
Cosine \(f(x)=\cos x\) Domain \(\{x\in\mathbb{R}\}\)
Range \(\{y\in\mathbb{R}\mid -1\le y\le 1\}\)
Parent cosine function