Functions

Lesson 2: 1 to 1 function

(1) What is a 1 to 1 function?

Let f be a function with domain X and range Y. f is said to be 1 to 1 if every value of x is mapped to exactly 1 value of y and every value of y belongs to exactly 1 value of x.

Not 1 to 1

1 to 1

(2) Checking if a function is 1 to 1

We can use the horizontal line test to check if a function is 1 to 1. Essentially every horizontal line y = k, where             cuts the graph of f exactly once.

Example 1

y = k

f is 1 to 1 since every horizontal line y = k, where           cuts the graph exactly once.

Example 2

g is not 1 to 1 since every horizontal line y = 1, cuts the graph more than once.

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