Module 6: Lesson 8 - Function and its Graph

Vocabulary flashcards defining fundamental function types, graph properties, and components based on Module 6 Lesson 8.

Function

A rule that assigns exactly one output to each input, represented as $y = f(x)$, where $y$ depends on $x$.

Linear Function

A function of the form $f(x) = mx + b$ whose graph is a straight line, characterized by a constant rate of change and a domain of all real numbers.

Slope ($m$)

The rate of change in a linear function $f(x) = mx + b$ that indicates steepness and direction: positive (rises left to right), negative (falls left to right), zero (horizontal), or undefined (vertical).

Absolute Value Function

A function defined as $f(x) = |x|$ that measures distance, with a V-shaped graph symmetrical about the vertical axis and a turning point at its vertex.

Quadratic Function

A function of the form $f(x) = ax^2 + bx + c$, where $a$, $b$, and $c$ are constants and $a \neq 0$, producing a parabola-shaped graph.

Parabola

The U-shaped curve that represents the graph of a quadratic function, opening upward when $a > 0$ and downward when $a < 0$.

Vertex

The turning point $(h, k)$ of a parabola, which is the minimum point if the parabola opens upward ($a > 0$) or the maximum point if it opens downward ($a < 0$).

Axis of Symmetry

A vertical line given by the formula $x = -\frac{b}{2a}$ that passes through the vertex and divides a parabola into two equal, symmetric halves.

Y-Intercept

The point where a graph crosses the y-axis, found by substituting $x = 0$ into the function (yielding $(0, c)$ for quadratic functions).

X-Intercepts

The points (also known as zeros or roots) where a graph crosses the x-axis, found by setting $f(x) = 0$.

Square Root Function

A function defined as $f(x) = \sqrt{x}$ with domain $x \ge 0$, starting at $(0,0)$ and gradually increasing.

Cube Root Function

A function defined as $f(x) = \sqrt[3]{x}$ characterized by an S-shaped curve, a domain of all real numbers, and passing through the origin.

Piecewise Function

A function defined by different rules or equations for different intervals of conditions within its domain.