Repeated Outputs vs. Repeated Inputs: What Breaks a Function?
Understanding what breaks a function in Algebra 1 (California Reveal Math, Grade 9): a relation is NOT a function only when the same input maps to two different outputs. Repeated outputs are perfectly allowed — multiple inputs can share the same output. For example, both (1, 4) and (3, 4) in a relation is fine (same output, different inputs). But (2, 5) and (2, 7) breaks the function definition (same input, different outputs). The vertical line test visually checks this: if any vertical line crosses the graph more than once, it is not a function.
Key Concepts
A relation is not a function only when the same input maps to two or more different outputs .
Repeated outputs are perfectly allowed:.
Common Questions
What makes a relation a function?
A relation is a function if every input (x-value) maps to exactly one output (y-value). No x-value can appear with two different y-values.
Can different inputs map to the same output in a function?
Yes. Multiple inputs can share the same output. For example, both x = 1 and x = -1 can map to y = 1 without breaking the function rule.
What specifically breaks a function?
If any single input maps to two or more different outputs, the relation is not a function. The issue is with repeated inputs having different outputs, not repeated outputs.
What is the vertical line test?
The vertical line test states: if any vertical line drawn on the graph intersects it more than once, the relation is not a function (one x-value maps to multiple y-values).
Where is the function definition taught in California Reveal Math Algebra 1?
This concept is introduced in California Reveal Math, Algebra 1, as part of Grade 9 functions and relations content.
Is a horizontal line y = 3 a function?
Yes. Every x-input maps to the same output (y = 3). Repeated outputs are fine.
What is a common example of a relation that is NOT a function?
A circle (x² + y² = r²) is not a function because any x-value between -r and r maps to two y-values (positive and negative square root).