1.1 Parent Functions, Domain and Range

Notes

A parent function is the simplest function of a family. Every other function in the family is a transformation of it.

• Key parents: linear $y = x$, quadratic $y = x^2$, cubic $y = x^3$, absolute value $y = |x|$, square root $\displaystyle y = \sqrt{x}$, reciprocal $\displaystyle y = \frac{1}{x}$.
• The domain is every input $x$ that works. The range is every output $y$ you get.
• Watch for two limits: you can't take an even root of a negative, and you can't divide by zero.
• Example: $\displaystyle f(x) = \sqrt{x - 3}$ needs $x - 3 \ge 0$, so the domain is $x \ge 3$ and the range is $y \ge 0$.