Cogito
Grade 8 Math · Chapter 6 · Lesson 1
What a Function Is
One output for every input.
10 problems · about 18 minutes · 8.F.A.1
What this lesson teaches
The child understands a function as a rule assigning exactly one output to each input.
- A function gives exactly one output for each input.
- The same input always gives the same output.
- Two outputs from one input means it is not a function.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Solving a System by Elimination: x + y = 12 and x − y = 4. What is x?
Answer 8
Why x = 8.
Review — Solving a System by Substitution: y = 4x and x + y = 15. What is x?
Answer 3
Why x = 3.
Warm Up
Straightforward practice. Get the method working first.
4 problemsRule "multiply by 4 then add 1". What comes out when 5 goes in?
Answer 21
Why 21.
What makes a rule a function?
Answer Every input has exactly one output.
Why Exactly one output per input.
Rule "multiply by 3". What comes out when 6 goes in?
Answer 18
Why 6 × 3.
Is "double it" a function?
Answer Yes.
Why One output each time.
Build It Up
The same ideas with more to keep track of.
2 problemsRule "subtract 4". What comes out when 10 goes in?
Answer 6
Why 10 − 4.
Can one input give two outputs in a function?
Answer No.
Why That is the definition.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Rule: The rule is "add 7". What comes out when 5 goes in?
Answer 12
Why 12.
The Test: A rule sends 4 to both 2 and −2. Is it a function?
Answer No. One input gave two outputs.
Why Not a function.