Which of the following represents a function?

Question

A.
A graph plots the points (negative 3, negative 2), (negative 1, 1), (negative 1, negative 5), and (1, 4) on the x y coordinate.
B.
{(0,1), (3,2), (-8,3), (-7,2), (3,4)}
C.
x -5 -1 9 8 -1
y 1 7 23 17 1
D.
A value negative 4 in the first ellipse corresponds to 5 in the second ellipse, a value 9 corresponds to 7, a value 13 corresponds to 3 and a value negative 7 corresponds to 5 in the second ellipse.

Answer 1

To determine which of the options represents a function, we need to remember the definition of a function: A function is a relation in which each input (or x-value) corresponds to exactly one output (or y-value).

Let's analyze each option:

A. A graph that plots the points (-3, -2), (-1, 1), (-1, -5), and (1, 4).

• Here, the x-value -1 corresponds to two different y-values (1 and -5). Therefore, this does not represent a function.

B. {(0,1), (3,2), (-8,3), (-7,2), (3,4)}

• In this set, the x-value 3 corresponds to two different y-values (2 and 4). Hence, this is not a function.

C.

x:   -5   -1    9    8   -1
y:    1    7   23   17    1

• The x-value -1 corresponds to two different y-values (7 and 1). Therefore, this is not a function.

D. A set of values as described:

• A value of -4 corresponds to 5, 9 corresponds to 7, 13 corresponds to 3, and -7 corresponds to 5.
  • Each x-value corresponds to exactly one y-value. Therefore, this represents a function.

Based on the analysis, the answer is:

D.