Transformations of Linear Equations

Vocabulary flashcards covering linear function transformations, including vertical shifts, vertical stretches, vertical compressions, and reflections based on the lecture notes and diagrams.

Parent Function $f(x) = x$

The foundational linear function $f(x) = x$ from which linear transformations such as vertical shifts, stretches, compressions, and reflections are formed.

Vertical Shift Up ($g(x) = x + 2$)

A transformation in which the graph of a function is translated vertically upward, such as $g(x) = x + 2$ which is shifted $2$ units up from $f(x)$.

Vertically Stretched Function ($f(x) = 2x$)

A transformation of the parent function $f(x) = x$ where the slope is multiplied by a factor greater than $1$, such as $f(x) = 2x$, causing the line to stretch vertically.

Vertically Compressed Function ($f(x) = \frac{1}{2}x$)

A transformation of the parent function $f(x) = x$ where the slope is multiplied by a factor between $0$ and $1$, such as $f(x) = \frac{1}{2}x$, causing the line to compress vertically.

Reflected Function ($f(x) = -x$)

A transformation of the parent function $f(x) = x$ where negating the equation creates $f(x) = -x$, reflecting the graph across the axis.