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