
2-16 Calculus – Differentiation and Integration
Figure 2.10
4
2
-2
-4 -3 -2 -1
4 3 2 1
Solution: Since we can draw a horizontal line that passes through two points, it is not one-to-one.
Similarly, we can draw a horizontal line, particularly, through the negative y-axis (this is possible
because the co-domain is the set of all real numbers) that does not intersect the graph at any point.
Hence, f is not onto.
Therefore, the function is not bijective.
Example 2.14 Test if the following graph is bijective.
-
4
-
3
-
2
-
1 1 2 3 4
4
2
-
2
-
4
Figure 2.11
Solution: The given graph passes the horizontal line test because every horizontal line ...