OBJECTIVES
1. Determining whether a function fits the definition of one-to-one

Objective 1: Determining Whether a Function fits the Definition of One-to-One

Definition: A function for which every element of the range of the function corresponds to exactly one element of the domain. A function is not one-to-one if two different elements in the domain correspond to the same element of the range.

Theorem: Horizontal line-Test
If every horizontal line intersects the graph of a function f(x) in at most one point, then f(x) is one-to-one.

Example 1a:
Does this table represent a one-to-one function? Why or why not?

Time (in hours) Yeast Cells
0 56
2 15
4 65
6 60
8 28

Solution 1a:
According to the definition, each input correlates to one and only one output. So, this is a one-to-one function.

Example 1b:
Does this table represent a one-to-one function? Why or why not?

Time (in hours) Yeast Cells
0 56
2 56
4 56
6 56
8 56

Solution 1b:
This table does not represent a one-to-one function because more than one input has the same output. Therefore, this is a function, but not a one-to-one function.

Practice Problems:

For Problems 1-5 assess each set of data and answer the question is this a one-to-one function?

1. {(1,4), (2,3), (-7,3)}
2. {(15,16), (34,27), (64,8)}
3. {(15,15), (10,15), (5,15)}
4. {(69,74), (54,75), (23,76)}
5. {(134,5), (123,7), (154,3)}

For Problems 6-10 graph each function and use horizontal-line test to determine whether f is one-to-one function:

6. f(x) = x
7. f(x) = x2
8. f(x) = x(½)
9. f(x) = xx
10. f(x) = ex