Question

The correspondence f: X- Yis defined by the function ((-18, -31), (-9, -23), (4, 2), (11, 5), (14, 12)). Consider the

correspondence g that includes the ordered pairs of f.
Which additional ordered pairs can be included in g, assuming g is a function. SELECT ALL THAT APPLY.
A(-9, 11)
B (-7,-10)
C (5, 12)
D (4, 15)
E (14,20)

Answer 1

B. (-7, -1)

C. (5, 12)

Explanation:

A function can only have one output for a specific input

In math terminology that means if y = f(x) is a function of x then the mapping from x to y is 1:1

Or,

For a specific value of x, there can be one and only one value for y

This is often referred to as a vertical line test; if a vertical line parallel to the y-axis is drawn for any x value it should intersect the function graph at one and only one point

g(x) includes all the ordered pairs of f(x) therefore the ordered pairs of g(x) are:
{ ( -18, -31), (-9, -23), (4, 2), (11, 5), (14, 12) }

Looking at the answer choices:
A. (-9, 11) will violate the 1:1 correspondence between x and y since (-9, -23) is already a pair

B. (-7, -1) is OK. There is no other entry with x = -7

C. (5, 12) is OK. There is no other entry with x = 5

D. (4, 15) will violate; there is already an entry for x = 4: (4, 2)

E. (14,20). This will also violate the properties of a function since there exists an entry for x = 14, namely (14, 20)