Based on the graph, all three relations are functions except graph 3.
A function is a mathematical relationship where for every input (x-value), there is only one output (y-value). In the graph, each point on the line has a unique y-value for a given x-value. Therefore, all three relations satisfy the definition of a function.
Here's a breakdown of each relation:
Relation 1: This relation is a straight line that increases as x increases. For each x-value, there is only one corresponding y-value on the line.
Relation 2: This relation is a curved line that starts low on the left side of the graph and rises to the right. For each x-value, there is only one corresponding y-value on the line.
Relation 3: This relation is a horizontal line that stays at the same y-value regardless of the x-value. While it might seem like there are multiple y-values for each x-value in this case, it's important to remember that a function is defined as a unique relationship between input and output. Since all the points on this line share the same y-value, it is still considered a function.