Piecewise Defined Functions Flashcards

Piecewise Defined Functions Overview

• Piecewise defined functions consist of different expressions based on specific intervals or conditions.
• Graph representations can help visualize and understand the rules governing these functions.

Card Summaries

• Graphing Piecewise Functions: Selecting the correct graph for a piecewise function is crucial for understanding its behavior.
• Continuity in Functions: Identifying continuous functions is important; not all piecewise functions are continuous due to abrupt changes in value.

Cost Function Example

• A cell phone plan includes a base cost covering a limited number of minutes, with additional charges for exceeding that limit.
• The cost structure is defined as a flat rate for the first 300 minutes and a per-minute fee thereafter.

Pricing Models in Piecewise Functions

• The cost of ordering towels can also be defined piecewise, with different rates applying for varying quantities ordered.
• For example, the first set is at a higher cost, and subsequent quantities are discounted.

Evaluation of Piecewise Functions

• Evaluating specific values from piecewise functions involves locating the appropriate segment of the graph.
• For instance, finding f(2) or f(5) in the given examples shows how to locate values based on specified x inputs.

Tax Rate Comparison

• Tax rates can also be defined piecewise based on income thresholds.
• For example, a tax plan may charge different percentages based on income brackets, demonstrating a practical application of piecewise functions.

Discontinuity in Functions

• Functions can exhibit discontinuities, with some being removable.
• Recognizing these discontinuities is important for analyzing function behavior graphically.

General Tips

• When analyzing piecewise functions, always pay attention to the defined intervals and respective expressions.
• Understanding how to graph piecewise functions and assess continuity will enhance function evaluation skills.