A function f is one-to-one (injective) if it never maps distinct elements of its domain to the same element of its codomain. That is, f(x₁) = f(x₂) implies x₁ = x₂.
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Pro Tips
Horizontal Line Test: If any horizontal line intersects the graph more than once, it is NOT one-to-one.
Strictly increasing or strictly decreasing functions are always one-to-one.
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Fun Facts
"One-to-one functions have inverses."
"The function f(x) = x² is NOT one-to-one on real numbers (since (-2)² = 2²)."
"The function f(x) = x³ IS one-to-one on real numbers."
