Week 3 — Functions: Notation, Domain & Range

Welcome to your Week 3 Start Here page.

Why this matters

A nurse reads one dose off a chart for each body weight, and a shop owner prices each order by one rule. Knowing which inputs a rule can accept keeps either of them from feeding it a value that breaks it.

In plain language

Press button 4 on a snack machine and one bag drops. Tell a bowl shop you want 3 toppings and the register shows one price, 13 dollars. This week you learn the math name for that kind of rule, a function (a rule that gives exactly one answer for each thing you put in). You will learn a short way to write a function, how to plug numbers and expressions into it, and how to tell which inputs it can accept, called its domain (the list of inputs that work). You will also learn its range (the list of answers it can give back), and how to chain two functions together so that one feeds the next.

• Already covered: Week 1's order of operations and Week 2's interval notation.
• This week: functions, function notation, domain and range, and combining and composing functions.
• How they connect: evaluating a function is Week 1's evaluation with a name, and a domain is written in Week 2's interval notation.
• Where we're going next: Week 4, Linear Functions & Their Graphs, reads a straight line as a function.

Focus

What goes into a rule, what comes out, and in what order do two rules run?

By the end of this module, you should be able to:

• [ ] tell whether a table or graph is a function
• [ ] evaluate f(−2) and g(a + 2) with parentheses first
• [ ] find a domain and read a range in interval notation
• [ ] add, subtract, multiply, divide, and compose two functions

To-do

Plan your week

1. Read Chapter 3 (about 45 minutes), then the lecture and the slides.
2. Work the lecture tutorial (60–90 minutes) and the practice set (about 20 minutes).
3. Do the Model/Build Studio (about 90 minutes), the discussion, and the assignment.
4. Take the quiz.

This week's checkpoint: evaluate f(x) = 3x² − 2x + 5 at x = −2 and find (f ∘ g)(−2) for g(x) = 3x + 4, inside first.

You've got this

Put every input in parentheses and work from the inside out, and ask your instructor early if a step snags.

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