In which of the following sets of points is y a function of x? A= {(2, 2), (4, 6), (5, 3), (5, 1)} B= {(2, 2), (3, 4), (4, 4), (5, 4)} C= {(1, 4), (2, 3), (4, 4), (4, 1)} D= {(1, 4), (1, 5), (2, 6), (3, 5)}
recall that if y=f(x) is a function, each x value must correspond to a single y value. No two distinct points may contain the same x value.
A fails: (5,3) and (5,1)
B works - distinct x values
C fails: (4,4) and (4,1)
D fails: (1,4) and (1,5)
To determine if y is a function of x in each set, we need to check if each x-value has a unique corresponding y-value.
Set A = {(2, 2), (4, 6), (5, 3), (5, 1)}
In this set, the x-value 5 has two corresponding y-values (3 and 1). Therefore, y is not a function of x in this set.
Set B = {(2, 2), (3, 4), (4, 4), (5, 4)}
In this set, each x-value has a unique corresponding y-value. Therefore, y is a function of x in this set.
Set C = {(1, 4), (2, 3), (4, 4), (4, 1)}
In this set, the x-value 4 has two corresponding y-values (4 and 1). Therefore, y is not a function of x in this set.
Set D = {(1, 4), (1, 5), (2, 6), (3, 5)}
In this set, the x-value 1 has two corresponding y-values (4 and 5). Therefore, y is not a function of x in this set.
So, the set in which y is a function of x is Set B.
To determine if y is a function of x in each of the given sets of points, we need to check if each x-value has a unique corresponding y-value.
A = {(2, 2), (4, 6), (5, 3), (5, 1)}
- In this set, the x-value 5 has two different y-values (3 and 1), so y is not a function of x.
B = {(2, 2), (3, 4), (4, 4), (5, 4)}
- In this set, each x-value has a unique y-value, so y is a function of x.
C = {(1, 4), (2, 3), (4, 4), (4, 1)}
- In this set, the x-value 4 has two different y-values (4 and 1), so y is not a function of x.
D = {(1, 4), (1, 5), (2, 6), (3, 5)}
- In this set, the x-value 1 has two different y-values (4 and 5), so y is not a function of x.
In summary, y is a function of x in set B, but not in sets A, C, and D.