Answer:
Based on the curve ; The graph is:
D. The curve is a many-to-one function.
Step-by-step explanation:
Function--
A function is a relation in which each element is mapped to a single element i.e. no element is mapped to two different elements.
Also, the graph of a function satisfies the vertical line test i.e. any line passing through the domain and parallel to the y-axis should intersect the graph exactly once.
and one-to-one function--
A one-to-one function is such that no two elements have the same image i.e. any line passing through the co-domain and parallel to the x-axis should intersect the graph at most once.
- The graph passes the vertical line test and hence is a function.
- Also, the graph of a linear function is a straight line.
Hence, by looking at the graph we see that the graph is not a straight line.
Hence, it is not a linear function.
- Also, it does not passes the horizontal line test (since somewhere in the interval (2,3) the same value is obtained many times )and hence it is not a one-to-one function
Hence, the correct answer is:
Option: D
