# Horizontal Line Test

- Author:
- mathtasksproj, Carlos

We say is a 1 to 1 function if whenever and we have . The mathematical term 'injective' is also used for these functions.
We say is an onto function if the range of is equal to . The mathematical term 'surjective' is also used for these functions.
On the following graph, adjust the values of to move the line and find points of intersection between the line and the function .

## Graph of f(x)

## 1A)

Is this function 1-1? Explain your answer.

## 2A)

Are there any intervals for which f(x) is 1-1?

## 3A)

Is this function onto? Explain why.

Now consider the function below:

## Graph of g(x)

## 1B)

Is this function injective? Explain your answer.

## 2B)

Are there any intervals for which f(x) is injective?

## 3B)

Is this function surjective? Explain why.

What features should a graph have in order to represent a 1-1 function? What about an onto function? Test your conjectures by entering a function in the graph below and applying the appropriate tests.

Write down your conjecture here.