
One to One Function
Range, Domain, horizontal line test

What is a 1 to 1 function?


How to know if f(x) is 1 to 1?

Practice Problems I
1)
Which functions below are 1 to 1?
Function #1 { (2,27), (3,28), (4,29), (5,30) }
Function #2 { (11,14), (12,14) , (16,7), (18,13) }
Function #3 { (3,12), (4,13), (6,14), (8,1) }
2)Which functions below are one to one ?
Function #1 { (2,1), (4,5), (6,7), (8,9) }
Function #2 { (3,6), (8,5), (6,7), (22,6) }
Function #3 { (3,4), (21,5), (0,0), (8,9) }
Function #4 { (9, 19), (34,5), (6,17), (8, 19) }
3) Is the function below a one toone function ?
Yes, because every element in the range is matched with only 1 element in the domain.

Practice Problems II
Use the horizontal line test and your knowledge of 1 to 1 functions to determine whether or not each graph below is 1 to 1 .
1)
Ask yourself:
"Can I draw a horizontal line (anywhere) that will hit the graph two times ?"
Since the answer is 'yes', this is not a onetoone function.
2)
Ask yourself:
"Can I draw a horizontal line (anywhere) that will hit the graph two times ?"
Since the answer is 'no', this is a onetoone function.
3)
Ask yourself:
"Can I draw a horizontal line (anywhere) that will hit the graph two times ?"
Since the answer is 'no', this is a 1 to 1 function.
4) Are all lines one to one like the prior problem was? If not, which types of lines are one to one and which types are not?
5) Are parabolas 1 to 1?
No
As the picture below shows, parabolas are not one to one
