Cogito
Algebra 1 · Chapter 3 · Lesson 2
Deciding What Is a Function
One input, one output — never two.
11 problems · about 21 minutes · F-IF.A.1
What this lesson teaches
The student decides whether a relation is a function from a graph, a table, or a mapping.
- A function gives exactly one output for every input.
- The vertical line test catches inputs with two outputs.
- Different inputs may share an output; that breaks nothing.
Warm Up
Straightforward practice. Get the method working first.
4 problemsInput 3 maps to both 1 and 8. Function? 1 for yes, 0 for no.
Answer 0
Why No.
A vertical line crosses a graph twice. Function? 1 for yes, 0 for no.
Answer 0
Why Two outputs for one input.
A horizontal line crosses a graph twice. Function? 1 for yes, 0 for no.
Answer 1
Why That tests something else entirely.
Is a circle a function? 1 for yes, 0 for no.
Answer 0
Why A vertical line hits it twice.
Build It Up
The same ideas with more to keep track of.
3 problemsIs y = 5 a function? 1 for yes, 0 for no.
Answer 1
Why Every input gives 5.
Sort each relation by whether it is a function.
Answer A function: y = 2x, y = x² · Not a function: x = 3, A circle
Why A vertical line is itself the classic failure.
Is x = 2 a function? 1 for yes, 0 for no.
Answer 0
Why One input, endless outputs.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsInputs 1, 2, 3 map to 4, 4, 4. Function? 1 for yes, 0 for no.
Answer 1
Why Repeated outputs are fine.
How many outputs may one input have in a function?
Answer 1
Why Exactly one.
The Repeat: Input 4 maps to both 7 and 9. Is it a function? 1 for yes, 0 for no.
Answer 0
Why No.
The Shared Output: Inputs 2 and 5 both map to 8. Is it a function? 1 for yes, 0 for no.
Answer 1
Why Yes.