Relations which are functions

Question

Hello experts, I have a question regarding this problem:

Determine whether or not each of the following relations represents y as a function of x.

Find the domain and range of those relations which are functions. a. (2, - 5) (3, 7) (2, 6) (4, 1) b. y = x3

I see that this is not a function due to the number 2 connects to the number - 5 and 6, but when finding the domain and range of relations that ARE functions should I also count 2, -5, and 6 or just list 3,4 and 7,1?

Answer 1

Hi, Gary,

For A, you are correct that it's not a function for the reason you gave. In this case, if it were a function, it's just a series of points, not a continuous line, so the domain is just a list of the x values (with no repetition), and the range is a list of the y values. I think this answers your question.

For item B, I assume you mean y = x³. If you sketch this function, you will see that it does not loop back on itself, so it is a function. Note also that there are no restrictions or empty spots for x, and likewise for y, so both the domain and range are all real numbers.

Best wishes!