Parent Functions Lecture Notes

Vocabulary flashcards covering the basic parent functions, their equations, and identifying characteristics based on the lecture transcript.

Parent Functions

The original, most basic form of a family of functions, representing the shape of the function before any transformations.

Constant Function

$f(x) = C$ (e.g., $f(x) = 2$).

Linear Function

$f(x) = x$.

Absolute Value Function

$f(x) = |x|$.

Quadratic Function

$f(x) = x^{2}$, which forms a shape typically called a parabola.

Square Root Function

$f(x) = \text{√}x$.

Cubic Function

$f(x) = x^{3}$.

Cube Root Function

$f(x) = \text{∛}x$ (notated as positive cube root).

Rational (Reciprocal) Function

$f(x) = \frac{1}{x}$, where the graph never touches the axes.

Reciprocal Squared Function

$f(x) = \frac{1}{x^{2}}$.

Logarithmic Function

$f(x) = \text{log}(x)$.

Exponential Function

$f(x) = b^{x}$.

Sine Function

$f(x) = \text{sin}(x)$, which starts at the center.

Cosine Function

$f(x) = \text{cos}(x)$, which starts in the "clouds" (at its peak).

Tangent Function

$f(x) = \text{tan}(x)$.