Piecewise Functions and Graph Transformations

Vocabulary and concept flashcards based on the provided worksheet covering piecewise functions, evaluations, domain, average rate of change, and transformations.

Domain of $f(x)$ in interval notation

$$[-5, -2) \cup [-2, 1] \cup (1, \infty)$$

Transformation $f(x + 2) - 3$

A transformation that shifts the graph of $f(x)$ horizontal left by $2$ units and vertical down by $3$ units.

Piecewise Function Evaluation $f(-3)$

$-3$, evaluated using the piece $-2x^2 + 15$ for the interval $-3 \le x < 10$

Piecewise Function Evaluation $f(1)$

$13$, evaluated using the piece $-2x^2 + 15$ for the interval $-3 \le x < 10$

Average Rate of Change (AROC)

The average rate of change of a function $f(x)$ over an interval $[a, b]$, calculated as $\frac{f(b) - f(a)}{b - a}$

Graph Transformation Worksheet Example

A worksheet section demonstrating piecewise function evaluations, domain determinations, and graph transformations such as $f(x + 2) - 3$