Which of the following is the graph of a one-to-one function?

• A.
• B.
• C.
• D.

Answer: (A)

Verified step by step guidance

1. Understand that a one-to-one function (also called an injective function) is a function where each output value corresponds to exactly one input value. This means no two different inputs produce the same output.
2. To determine if a function is one-to-one, you can use the Horizontal Line Test: if any horizontal line intersects the graph of the function more than once, the function is not one-to-one.
3. Alternatively, algebraically test if the function is one-to-one by assuming \( f(a) = f(b) \) and then showing that this implies \( a = b \). If this is true for all \( a \) and \( b \), the function is one-to-one.
4. If the function is given explicitly, try to solve the equation \( f(a) = f(b) \) for \( a \) and \( b \). If the only solution is \( a = b \), then the function is one-to-one.
5. Remember that one-to-one functions have inverses that are also functions. So, checking if the inverse exists and is a function can also confirm one-to-one behavior.