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Patterns, Functions, and Algebra
Session 5 Part A Part B Part C Part D Part E Homework
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Notes for Session 5, Part D

Note 14

The point of this section is to make connections between the different situations in which we've seen linear functions.

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Note 15

Take 15-20 minutes to work on Problems D1-D7. Then think about the connections in the different representations, paying particular attention to instances where linear functions are different from other kinds of functions.

In Problem D6, the recursive rule for the function y = 1/x can be quite challenging. The easiest way to describe it is to use your input in the rule.

output = (previous output) * (input - 1) / (input) or output = (previous output) - 1/ (input-1) (output)

Some people consider a rule recursive only if it truly depends on previous outputs, with no reference to the input.

In summary:


Closed forms for linear functions look like y = ax + b, where a and b are some numbers, x is the independent variable, and y is the dependent variable.


Recursive rules for linear functions add a constant value from one output to the next. This constant is the same as the value of a in the formula y = ax + b.


Graphs of linear functions look like lines. The slopes of the lines are the same as the difference between successive outputs, and the same as the value of a in the y = ax + b formula.

Groups: Discuss the above statements.

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