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. Step 1: Understand the definition of a one-to-one function. A function is one-to-one if each output (y-value) corresponds to exactly one input (x-value). This means no horizontal line should intersect the graph more than once.
2. Step 2: Apply the horizontal line test to each graph. Imagine drawing horizontal lines across the graph and check how many times each line intersects the graph.
3. Step 3: For the first graph (a diagonal line descending from upper left to lower right), any horizontal line will intersect the graph only once, indicating it is one-to-one.
4. Step 4: For the second graph (a downward-opening parabola), some horizontal lines will intersect the graph twice, so it is not one-to-one.
5. Step 5: For the third graph (a curve opening rightward), some horizontal lines will intersect the graph twice, so it is not one-to-one. For the fourth graph (a circle), many horizontal lines intersect the graph twice, so it is not one-to-one.