Function Families Vocabulary Flashcards

Vocabulary flashcards covering basic function families, parent equations, graph shapes, and key characteristics.

Identity / Linear Function

A function family with parent equation $f(x) = x$ and graph shape Line.

Absolute Value Function

A function family with parent equation $f(x) = |x|$ (or piecewise $f(x) = \begin{cases} -x & \text{if } x < 0 \\ x & \text{if } x \ge 0 \end{cases}$) and graph shape V-shape.

Quadratic Function

A function family with parent equation $f(x) = x^2$ and graph shape Parabola.

Cubic Function

A function family with parent equation $f(x) = x^3$ and graph shape reflected S-shape.

Square Root Function

A function family with parent equation $f(x) = \sqrt{x}$ and graph shape top half of a sideways parabola.

Cube Root Function

A function family with parent equation $f(x) = \sqrt[3]{x}$ and graph shape S-shape.

Exponential Function

A function family with parent equation $f(x) = b^x$ (e.g., $f(x) = 10^x$) and graph shape J-shape.

Logarithmic Function

A function family with parent equation $f(x) = \log_b(x)$ (e.g., $f(x) = \log(x)$) and graph shape reflected J-shape.

Rational / Reciprocal Function

A function family with parent equation $f(x) = \frac{1}{x}$ and graph shape hyperbola.

Euler's Number ($e$)

Also called the natural base, a base frequently used in exponential functions.

Inverse of $y = 10^x$

The logarithmic function $f(x) = \log(x)$, where all inputs and outputs switch.

Inverse of $y = e^x$

The natural logarithmic function $y = \ln(x)$.

Horizontal Line Linear Function

A linear function formatted as $f(x) = c$, where $c$ is any real number, producing a horizontal line with y-intercept $c$.

Graph of Identity / Linear Function

The graph representing $f(x) = x$ with shape Line.

Graph of Absolute Value Function

The graph representing $f(x) = |x|$ with shape V-shape.

Graph of Quadratic Function

The graph representing $f(x) = x^2$ with shape Parabola.

Graph of Cubic Function

The graph representing $f(x) = x^3$ with shape reflected S-shape.

Graph of Square Root Function

The graph representing $f(x) = \sqrt{x}$ with shape top half of a sideways parabola.

Graph of Cube Root Function

The graph representing $f(x) = \sqrt[3]{x}$ with shape S-shape.

Graph of Exponential Function

The graph representing $f(x) = b^x$ with shape J-shape.

Graph of Logarithmic Function

The graph representing $f(x) = \log_b(x)$ with shape reflected J-shape.

Graph of Rational / Reciprocal Function

The graph representing $f(x) = \frac{1}{x}$ with shape hyperbola.