Question

Based on the graph below, how would you describe the curve?

A. The curve is a linear function
B. The curve is a "many-to-one" function.
C. The curve is a "one-to-one" function.
D. The curve is not a function.

Answer 1

Based on the curve ; The graph is:

B. The curve is a many-to-one function.

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: B