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
{(1, 2), (2, 3), (3, 5), (4, 7), (5, 11), (6, c)}
a. 2
b. 5
c. 11
d. 13
Answers
GPT 3.5
d. 13
For a function to be one-to-one, every element in the domain must correspond to a unique element in the range. In this case, every x-value in the domain corresponds to a unique y-value in the range EXCEPT for (6, c) and (7, c).
Therefore, the function will be one-to-one if the value of c is different from the other y-values. Since the other y-values are 2, 3, 5, 7, and 11, the value of c must be 13 for the function to be one-to-one.
For a function to be one-to-one, every element in the domain must correspond to a unique element in the range. In this case, every x-value in the domain corresponds to a unique y-value in the range EXCEPT for (6, c) and (7, c).
Therefore, the function will be one-to-one if the value of c is different from the other y-values. Since the other y-values are 2, 3, 5, 7, and 11, the value of c must be 13 for the function to be one-to-one.