Parent Functions - CC+ College Algebra

Vocabulary flashcards covering equations, graphs, domains, and ranges of parent functions and conic sections from College Algebra.

(Increasing) Line Parent Function

The linear parent function given by $y = x$ (or $y = 1x + 0$), with domain $(-\infty, \infty)$ and range $(-\infty, \infty)$.

Parabola Parent Function

The quadratic parent function given by $y = x^2$, with vertex at $(0, 0)$, domain $(-\infty, \infty)$, and range $[0, \infty)$.

Cubic Function Parent Function

The parent function given by $y = x^3$, with domain $(-\infty, \infty)$ and range $(-\infty, \infty)$, passing through the origin $(0, 0)$.

Square Root Function Parent Function

The parent function given by $y = \sqrt{x}$ located in Quadrant 1, starting at $(0, 0)$, with domain $[0, \infty)$ and range $[0, \infty)$.

Hyperbola Parent Function

The parent rational function given by $y = \frac{1}{x}$ whose graph does not touch the axes, featuring domain $(-\infty, 0) \cup (0, \infty)$ and range $(-\infty, 0) \cup (0, \infty)$.

Inverse-Square Function Parent Function

The parent function given by $y = \frac{1}{x^2}$ whose graph does not touch the axes, with domain $(-\infty, 0) \cup (0, \infty)$ and range $(0, \infty)$.

Unit Circle

The relation defined by $x^2 + y^2 = 1$ with center $(0, 0)$ and radius $r = 1$, possessing domain $[-1, 1]$ and range $[-1, 1]$; it is not a function.

Semicircle (Centered at Origin)

The parent function given by $y = \sqrt{r^2 - x^2}$ (derived from $x^2 + y^2 = r^2$), with domain $[-r, r]$ and range $[0, r]$.

Equation of Any Circle

The standard form equation given by $(x - h)^2 + (y - k)^2 = r^2$, which yields $x^2 + y^2 = 1$ when centered at $(0, 0)$ with radius $r = 1$.