Summary
Highlights
A one-to-one function is defined as a function where each x-value (domain) maps to exactly one unique y-value (range). We use mapping diagrams to illustrate this concept. If two different x-values map to the same y-value, it is not a one-to-one function.
When given ordered pairs, a function is one-to-one if there are no two distinct inputs that correspond to the same output. This means that all y-values in the ordered pairs must be unique.
For equations, a function f(x) is one-to-one if f(x1) = f(x2) implies x1 = x2. A simpler rule is that if the highest degree (exponent) of the function is an odd number, it's generally a one-to-one function. If the highest degree is an even number, it is generally not a one-to-one function (e.g., x^2 gives the same output for positive and negative inputs).
Real-life situations can help explain one-to-one functions. Examples include a driver's license number to a person (one-to-one) or an SSS member to their SSS number. However, a person to their citizenship is not one-to-one if dual citizenship is possible. Similarly, distance traveled in a jeepney to the fare is not one-to-one because different distances might have the same fare.
For graphs, the horizontal line test is used. If any horizontal line intersects the graph of a function at most once, then the function is one-to-one. If a horizontal line intersects the graph at more than one point, it is not a one-to-one function.