Which graph does Not represent y as a function of x
A graph that does not represent y as a function of x is one where a vertical line intersects the graph at more than one point. If there is a vertical line that intersects the graph at more than one point, it implies that for a single x-value, there are multiple y-values. This violates the definition of a function, which states that for every input x, there must be exactly one output y. Therefore, a graph with a vertical line intersecting at more than one point does not represent y as a function of x.
To determine which graph does not represent y as a function of x, we need to understand the concept of a function.
In mathematics, a function is a relation between a set of inputs (called the domain) and a set of outputs (called the range), such that each input has exactly one corresponding output. In other words, for any given input value, there should be only one output value.
Now, to identify a graph that does not represent y as a function of x, we need to check if there are any occurrences of a single x-value having multiple y-values. This violates the definition of a function because it indicates that one input has multiple outputs, which is not allowed.
To do this, analyze each graph by following these steps:
1. Check if there are any vertical lines that intersect the graph in more than one point. If such lines exist, it means that a single x-value has multiple y-values, hence it is not a function.
2. Alternatively, you can use the "Vertical Line Test." Imagine drawing a vertical line through the graph. If the vertical line intersects the graph in more than one point, then it does not satisfy the definition of a function.
By applying either of these methods to the given graphs, you can identify the graph that does not represent y as a function of x.