Chapter 4 - An Introduction to Functions - 4-6 Formalizing Relations and Functions - Practice and Problem-Solving Exercises - Page 272: 30

Any x value will make the relation function except the values of 1 and -7.

The relation {(1, 5), (x, 8), (-7, 9)} will be a function for any x value except 1 and -7 because if x is 1 then the set becomes {(1, 5), (1, 8), (-7, 9)} which does not pass the vertical line test as there are two y values for one value of x as at x=1, y=5,8. Also if x=7 then the set becomes {(1, 5), (7, 8), (-7, 9)} which does not pass the vertical line test as there are two y values for one value of x as at x=7, y=8,9. Therefore at any x-value except 1 and -7, the following relation will be a function because for each x value there will be one y-cordinate value. Thus the relation would pass the vertical line test as there would be no two y values for one x values and therefore the relation would be a function.