Function Machines: Two-Step Operations And Output Comparison.pdf

Understanding the Concept:

A function machine takes an input number, applies a specific mathematical operation (the rule), and produces an output number. A two-step function machine uses two consecutive operations.

Two-Step Function Machine Examples:

1. Example: x 5 + 2

Step 1: Multiply the input by 5.
Step 2: Add 2 to the result from Step 1.

2. Example: – 1 × 3

Step 1: Multiply the input by 3.
Step 2: Subtract 1 from the result of Step 1.

Table Completion and Verification:

Completing Tables: Fill in missing outputs for given inputs using the defined rules.
Reverse Order: Reverse the steps to check if the same output is produced when input and output are switched.
Partner Explanation: Discuss reasoning with a partner to ensure understanding of each step's contribution to the final output.

Identifying Consistent Output Pairs:

Same Outputs: Identify function machine pairs that always produce the same output for a given input (e.g., + 4 + 3 and + 3 + 4).
Different Outputs: Highlight pairs that consistently produce different outputs (e.g., – 1 × 3 and × 3 – 1).

Simplifying Two-Step Machines:

Single Step Equivalents: For each two-step machine, determine a single step operation that yields the same output (e.g., × 2 × 5 can be simplified to × 10).

Discussion:

Comprehensiveness: Can all two-step function machines be represented as one-step functions? Discuss with a partner, considering examples and potential limitations.

Real-World Application:

Online Photo Order:

* Analyze a function machine representing photo ordering (e.g., × 4 – 3) to determine pricing based on the number of photos ordered.