11th Grade Q1

A function is one-to-one if each input has a unique output, and each output comes from only one input. This means no two inputs can produce the same output.

Example 1

Imagine an app subscription plan where the cost depends on the number of months you subscribe:

Here:

• $x$ is the number of months.
• $f(x)$ is the total cost in dollars.

If you subscribe for 1 month, the cost is 10. For 2 months, it’s 20. Each input ($x$) gives a unique output ($f(x)$), so this is a one-to-one function.

Example 2

Consider a situation where students take a test, and multiple students can receive the same score. Let $f(x)$ represent the score of a student $x$.

For example:

• Student $1$ scores 85.
• Student $2$ scores 85.
• Student $3$ scores 90.

Here, different inputs (students) can have the same output (test scores). In particular, $x=1$ and $x=2$ have the same output, $f(1)=85=f(2)$. This is not a one-to-one function because one output corresponds to more than one input.