Evaluating and graphing piecewise functions | Math | Rimetric Walkthrough

Master Piecewise Functions: Evaluating, Graphing & Finding Domain/Range! 📈✂️ What happens when a single mathematical function changes its rule depending on the input you give it? In this Rimetric Walkthrough, we dive into the versatile world of Piecewise Functions! From tax brackets to tiered utility bills, real-world math depends on these multi-rule relationships. We start by decoding piecewise notation and understanding the critical requirement of mutually exclusive conditions—proving why overlapping boundaries break the definition of a function! Then, we tackle step-by-step evaluations using multi-branch examples (including quadratics, linear lines, and rational functions). Finally, we unify everything by calculating domain and range across split intervals and constructing full piecewise graphs using open ( ) and closed [ ] boundary circles. Graphing Linear function -    • Understanding linear functions, equations,...   Graphing Quadratic function -    • Solving quadratic functions, equations, an...   📌 What You’ll Learn: Decoding Piecewise Notation: Reading curly brackets, branches, and domain conditions correctly. The Single-Output Rule: Why overlapping conditions that yield different outputs fail the function test. Step-by-Step Evaluation: Knowing which branch to choose for inputs inside, outside, or right on boundary endpoints (and identifying when a function is undefined). Domain & Range Across Branches: Using interval notation, unions, and extreme points/vertices to determine exact output boundaries. Assembly-Style Graphing: Plotting parabolas, straight lines, and rational curves over specific restricted intervals. Open vs. Closed Boundary Circles: Knowing when to place an open circle for strictly less/greater than versus a solid dot for inclusive inequalities. ----------------------------------------------------------------------- Timestamps 0:00 Intro 0:42 Piecewise function 1:36 Solution 3:33 Example 2 5:45 Domain 7:08 Range 13:24 Graph 16:48 Outro ------------------------------------------------------------------------ Love our walkthrough style? Hit that SUBSCRIBE button to join the Rimetric Walkthrough community, and leave a comment below if you want us to cover a specific math topic in our next video!