Algebra

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# One to One Function

#### Lesson Contents

## What is a One to One Function?

**Also known as an injective function, a one to one function is a mathematical function that has only one y value for each x value, and only one x value for each y value.**

Let’s take y = 2x as an example. Plugging in a number for *x* will result in a single output for *y*. Also, plugging in a number for *y* will result in a single output for *x*. Both conditions hold true for the entire domain of y = 2x. Therefore, y = 2x is a one to one function.

Now let’s take y = x^{2} as an example. Plugging in any number for *x* along the entire domain will result in a single output for *y*. However, plugging in any number for *y* does not always result in a single output for *x*. For instance, at y = 4, x = 2 and x = -2. Therefore, y = x^{2} is a function, but not a one to one function.

### How to Test if it's a One to One Function

**A one to one function passes the vertical line test and the horizontal line test.** The first step is to graph the curve or visualize the graph of the curve.

To perform a vertical line test, draw vertical lines that pass through the curve. For the curve to pass the test, each vertical line should only intersect the curve *once*. Passing the vertical line test means it only has one y value per x value and is a function.

The horizontal line test is the vertical line test but with horizontal lines instead. For the curve to pass, each horizontal should only intersect the curve *once*. Passing the horizontal line test means it only has one x value per y value.