What is a one to one function?
A function is considered one to one if no two elements in the domain of function F correspond to the same element in the range of function F. Another way to say it, is that each x in the function F has exactly one y value in the range function F.
How to identify a one to one function:
A function is considered one to one if no two elements in the domain of function F correspond to the same element in the range of function F. Another way to say it, is that each x in the function F has exactly one y value in the range function F.
How to identify a one to one function:
To identify a one to one function, you can use the Horizontal Line Test.
First graph your function that you want to test such as f(x) =
First graph your function that you want to test such as f(x) =
Then draw a horizontal line. If the horizontal line only hits the function once, then the function can be identified as being one to one.
But if the horizontal line hits the function more than once as see in the function f(x) =
, then the function is declared as NOT being one to one
Sample Math Problems
1. Use the horizontal line test to identify if the following function is one to one.
Solution: Yes this function is a one to one function. At every point where there is a horizontal line, the line only intersects with one point on the graph f(x) = 1/x
2. Which of these is a one to one function?
a) f=(1,2),(3,4),(5,6),(8,6),(10,−1)
b) f=(−1,2),(0,4),(2,−4),(5,6),(10,0)
c) f=(1,2),(3,4),(5,6),(8,6),(10,6)
d) f=(−1,2),(0,−4),(2,−4),(5,6),(10,2)
Solution: B – because the coordinates, there is only one y value for every x value.
3. Is function f defined by f = {(1 , 2),(3 , 4),(5 , 6),(8 , 6),(10 , -1)} a one to one function?
Solution: No, because two points in the domain 5 and 8 have the same output and hence the function is not one to one
4. Is function x defined by x = {(-1 , 2),(0 , 4),(2 , -4),(5 , 6),(10 , 0)} a one to one function?
Solution: Yes, because all points in the domain have different outputs and hence the function is one to one.
