Introduction to piecewise functions

Описание: *CORE CONCEPT:*
Piecewise functions are defined by different expressions based on the input value (x). Understanding how to evaluate and graph these functions is essential for B1 level students.

*TOPICS COVERED:*
When to use piecewise functions to define different behaviors based on conditions.
How to evaluate piecewise functions by substituting values into the correct piece.
How to graph piecewise functions using linear segments for different intervals.

*GRAMMAR RULES:*
Determine which interval → identify the correct piece of the function.
Use the corresponding function rule → calculate the output value (f(x)).
If necessary → plot the point on a graph and connect the segments.

*COMMON ERRORS:*
Wrong: Mixing up conditions and using an incorrect function piece. → Right: Check the interval conditions before substituting values.

*STUDENT QUESTIONS:*
How do I evaluate a piecewise function?
When do I use the different pieces of a piecewise function?
Is my evaluation of f(1) correct?
What's the difference between piecewise functions and regular functions?
How do I graph a piecewise function?

*KEY CONCEPTS:*
Piecewise functions, evaluation, graphing, B1 level, function rules, intervals, conditions.