Function Transformations and Linear Models

Vocabulary flashcards covering graph interpretation, linear functions, and function transformations including reflections, stretches, and translations.

Tank Temperature at $h = 0\text{ hours}$

The initial temperature of the tank shown on the graph, which is $82^\circ\text{F}$.

Decreasing Behavior (Tank Temperature)

The characteristic of the function showing that the tank temperature drops over time, decreasing by two degrees each hour.

Vertical Translation Down $3$

The transformation given by $g(x) = f(x) - 3$, which shifts the graph of $f(x) = 2x - 5$ downward by $3$ units to produce $g(x) = 2x - 8$.

Reflection Over the $x$-Axis

The transformation given by $g(x) = -f(x)$, which reflects the graph across the $x$-axis, changing $f(x) = 2x - 1$ into $g(x) = -2x + 1$.

Vertical Stretch by $3$

The transformation defined by $g(x) = 3f(x)$, which vertically stretches the graph of $f(x)$ by a factor of $3$.

Horizontal Stretch of $3$

The transformation where modifying the input of $f(x)$ results in stretching the graph horizontally by a factor of $3$.

Vertical Translation Up $5$

The transformation represented by $g(x) = f(x) + 5$, which shifts the graph of $f(x)$ upward by $5$ units.

Horizontal Translation Right $8$

The transformation represented by $g(x) = f(x - 8)$, which shifts the graph of $f(x)$ to the right by $8$ units.