General Mathematics — Functions Reviewer

Vocabulary flashcards covering linear, quadratic, cubic, square root, cube root, and absolute value functions based on the lecture reviewer.

Linear Function

A polynomial function with a highest exponent of $1$, whose graph is always a straight line with a constant rate of change.

General Form of a Linear Function

$f(x) = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Slope ($m$)

The measure of steepness of a line calculated as $m = \frac{\text{Rise}}{\text{Run}}$, where a positive slope rises and a negative slope falls.

Quadratic Function

A polynomial function with a highest exponent of $2$, whose graph forms a parabola.

General Form of a Quadratic Function

$f(x) = ax^2 + bx + c$, where $a \neq 0$.

Vertex Form of a Quadratic Function

$f(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex and $x = h$ is the axis of symmetry.

Parabola

The U-shaped or $\cap$-shaped graph of a quadratic function, opening upward if $a > 0$ and downward if $a < 0$.

Cubic Function

A polynomial function with a highest exponent of $3$, whose graph generally exhibits an S-shaped appearance.

General Form of a Cubic Function

$f(x) = ax^3 + bx^2 + cx + d$, where $a \neq 0$.

Transformation Form of a Cubic Function

$f(x) = a(x - h)^3 + k$, derived from parent function $f(x) = x^3$.

Square Root Function

A function containing a variable under a square-root symbol, with general form $f(x) = a\sqrt{x - h} + k$.

Endpoint (Square Root Function)

The starting point $(h, k)$ of a square root function graph, from which the curve extends.

Domain Restriction of a Square Root Function

The requirement that the expression inside the radical cannot be negative, giving a domain of $x \geq h$ for $f(x) = a\sqrt{x - h} + k$.

Cube Root Function

A function containing a variable inside a cube-root radical, with general form $f(x) = a\sqrt[3]{x - h} + k$.

Inflection Point (Cube Root Function)

The center point $(h, k)$ of a cube root function graph, which forms a sideways S-shaped curve.

Absolute Value Function

A function representing the distance of a number from zero, with general form $f(x) = a|x - h| + k$ and a V-shaped graph.

Vertical Stretch (Absolute Value)

A transformation occurring when $a > 1$ in $f(x) = a|x - h| + k$, making the V-shaped graph steeper.

Vertical Compression (Absolute Value)

A transformation occurring when $0 < a < 1$ in $f(x) = a|x - h| + k$, making the V-shaped graph wider.

Reflection (Absolute Value)

A transformation occurring when $a < 0$ in $f(x) = a|x - h| + k$, causing the graph to reflect downward.

Horizontal Shift

A transformation controlled by the value $h$ in standard function forms, shifting the graph horizontally.

Vertical Shift

A transformation controlled by the value $k$ in standard function forms, shifting the graph vertically.