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Goals : Write a function rule given a table or a real-world situation.

Algebra Chapter 5: Graphs and Functions Lesson 5-4: Writing a Function Rule Lesson 5-6: Describing Number Patterns. Goals : Write a function rule given a table or a real-world situation. Use inductive reasoning in continuing number patterns. Write rules for arithmetic sequences.

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Goals : Write a function rule given a table or a real-world situation.

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  1. AlgebraChapter 5: Graphs and FunctionsLesson 5-4: Writing a Function RuleLesson 5-6: Describing Number Patterns Goals: Write a function rule given a table or a real-world situation. Use inductive reasoning in continuing number patterns. Write rules for arithmetic sequences.

  2. Independent and Dependent Variables • Independent variable: The inputs are values of the independent variable. • Dependent variable: The outputs are the corresponding values of the dependent variable.

  3. Writing a Function Rule • We can write a rule for a function by analyzing a table of values. • Look for a pattern relating the independent and dependent variables. • When we write a function rule, the dependent variable is defined in terms of the independent variable.

  4. Inductive Reasoning • Inductive reasoning is making conclusions based on patterns that can be observed. • A conclusion reached by inductive reasoning is a conjecture.

  5. Sequences • A number pattern is also called a sequence. Each number in a sequence is a term of the sequence. • An arithmetic sequence is formed by adding a fixed number, called the common difference, to each previous term. The formula for the nth term of an arithmetic sequence is A(n) = a + (n – 1) d, where A(n) is the nth term, a is the first term, and d is the common difference.

  6. Assignments and a Note: • Class work: Worksheet. • Homework 5-4: #3 – 18, (every 3rd) and HW 5-6: #5 - 40 (every 5th). • Test next Tuesday.

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