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Graphing piecewise non-linear functions

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Mathematics Essentials 11
Patterns and Relations
7. Model real-world problems using functions, equations, inequalities and discrete structures
7.13 Graphing piecewise non-linear functions

Graphing piecewise non-linear functions

What You'll Learn

Graph piecewise functions with nonlinear components like parabolas, cubics, and square roots
Apply domain restrictions to nonlinear functions and identify open vs. closed endpoints
Determine domain and range of piecewise nonlinear functions using graphical analysis
Graph absolute value functions by reflecting negative portions vertically
Express absolute value functions as piecewise functions with appropriate domains

What You'll Practice

1

Sketching piecewise functions with parabolas, cubics, reciprocals, and radical functions

2

Finding domain and range from graphs using interval and set notation

3

Converting absolute value functions into equivalent piecewise definitions

4

Graphing transformations of nonlinear functions with restricted domains

Why This Matters

Piecewise nonlinear functions model real-world situations where relationships change at different thresholdslike tax brackets, shipping rates, or water pressure at varying depths. Mastering these graphs builds your ability to analyze complex functions in calculus and applied math.

Before You Start — Make Sure You Can:

Graphing parabolas for given quadratic functionsGraphing exponential functionsGraphing piecewise linear functionsDomain and range of a function

This Unit Includes

13 Video lessons

Skills

Piecewise Functions
Nonlinear Graphs
Domain and Range
Absolute Value
Parabolas
Cubic Functions
Transformations
Graphing
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