To determine if a graph is one to one (often written as 1-1), you can use the Horizontal Line Test. This test states that a function is one to one if no horizontal line intersects the graph more than once.
Here’s how to apply the test:
- Draw horizontal lines across various parts of the graph.
- If any horizontal line touches the graph at more than one point, then the graph is not one to one.
- If every horizontal line crosses the graph at most once, then it is classified as one to one.
The horizontal line test is particularly useful for identifying functions that have a unique output for every input. For example, the function f(x) = x^2 is not one to one because a horizontal line at y = 4 intersects the graph at both x = 2 and x = -2.
On the other hand, the graph of the function f(x) = x is one to one since any horizontal line will only intersect the graph at one point.
Using this simple method helps in visualizing and confirming whether a function’s outputs are unique for its inputs, a fundamental concept in functions and relations.