Question

For what value of c is the function one-to-one? {(1, 2), (2, 3), (3, 5), (4, 7), (5, 11), (6, c)}

A) 2
B) 5
C) 11
D) 13

Answer 1

The function is one-to-one if c = 11.

Step-by-step explanation:

A function is said to be one-to-one if each element in the domain is paired with a unique element in the range. In other words, no two different elements in the domain can have the same image in the range. To determine if the given function is one-to-one, we need to check if any two points in the set of ordered pairs have the same y-coordinate.

Let's check:

(1, 2) and (2, 3) have different y-coordinates, so they don't violate the one-to-one condition.

(2, 3) and (3, 5) have different y-coordinates.

(3, 5) and (4, 7) have different y-coordinates.

(4, 7) and (5, 11) have different y-coordinates.

(5, 11) and (6, c) can have the same y-coordinate if c = 11. But if c is any other value, the y-coordinates will be different.

Therefore, the function is one-to-one if c = 11.