Question

Which explains why the graph is not a function?

a) It is not a function because the points are not connected to each other.
b) It is not a function because the points are not related by a single equation.
c) It is not a function because there are two different x-values for a single y-value.
d) It is not a function because there are two different y-values for a single x-value.

Answer 1

The correct answer is option d) It is not a function because there are two different y-values for a single x-value, which fails the vertical line test for functions.

Step-by-step explanation:

To determine whether a graph represents a function, one must check that every x-value on the graph maps to exactly one y-value, which is known as the vertical line test. When there are two different y-values for a single x-value, the vertical line test is failed, indicating that the graph does not represent a function.

Therefore, the correct answer is: d) It is not a function because there are two different y-values for a single x-value.

Line graphs typically show the relationship between two variables, with one measured on the horizontal axis (the x-axis) and the other on the vertical axis (the y-axis). A function's graph must pass the vertical line test, meaning that a vertical line drawn at any x-value on the graph would cross the graph at exactly one point.