Cogito
Algebra 1 · Chapter 3 · Lesson 1
Function Notation, Domain, and Range
A name for the rule, and the numbers it accepts.
10 problems · about 19 minutes · F-IF.A.1, F-IF.A.2, F-IF.B.5
What this lesson teaches
The student uses function notation, evaluates functions, and identifies domain and range.
- f(x) names a rule; f(3) is its value at 3.
- The domain is the allowed inputs, the range is the outputs.
- f(3) is not multiplication.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Inequalities in Two Variables: Does (0, 0) satisfy y < x − 3? 1 for yes, 0 for no.
Answer 0
Why No.
Review — Inequalities from Situations: £60 with books at £7. How many at most?
Answer 8
Why 8.
Warm Up
Straightforward practice. Get the method working first.
4 problemsf(x) = 6x − 7. What is f(3)?
Answer 11
Why 11.
What is the domain of a function?
Answer The set of allowed inputs.
Why Domain is the inputs.
f(x) = 5x − 2. What is f(4)?
Answer 18
Why 20 − 2.
f(x) = x² + 1. What is f(3)?
Answer 10
Why 9 + 1.
Build It Up
The same ideas with more to keep track of.
2 problemsf(x) = 3x + 1 and f(a) = 16. What is a?
Answer 5
Why 3a = 15.
Does f(3) mean f multiplied by 3?
Answer No. It is the value of f at 3.
Why The brackets are not multiplication here.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsEvaluating: f(x) = 4x + 3. What is f(6)?
Answer 27
Why 27.
Working Backwards: f(x) = 2x − 5 and f(a) = 9. What is a?
Answer 7
Why a = 7.