Classifying Functions by Their Equations and Graphs

Vocabulary flashcards covering the definitions, notation, graph shapes, and key features of cubic, square root, and cube root functions.

Cubic Function

A function that has a variable raised to the third power, such as $x^3$.

Cubic Function Graph Shape

An S-shaped curve that moves from lower-left to upper-right and passes through the origin in its basic form.

Square Root Function

A function where the variable appears inside a square root symbol, such as $\sqrt{x}$.

Square Root Function Graph Shape

A curve that starts at an endpoint (usually zero) and curves upward to the right, having no negative $x$-values.

Cube Root Function

A function where the variable appears inside a cube root symbol, such as $\sqrt[3]{x}$.

Cube Root Function Graph Shape

An S-shaped curve that extends both left and right, passing through the origin in its basic form.

Distinguishing Cubic and Cube Root Graphs

Because both cubic and cube root graphs are S-shaped, equation notation is the decisive clue to distinguish between them.

Domain of Cube Root Functions

Cube roots accept both negative and positive $x$-values.

Horizontal Shifts in Square Root Functions

Transformations that move the graph's starting point or endpoint horizontally.

Transformations of Cubic Functions

Shifts and stretches that affect the cubic graph's shape and position while retaining a cubic term.