Which of the following graphs is not a function? This question often arises in mathematics, particularly when dealing with the concept of functions. A function is a relation between a set of inputs and a set of permissible outputs, where each input is related to exactly one output. In this article, we will explore the characteristics of functions and identify the graph that does not represent a function.
In mathematics, a function can be represented by a graph, where the input values are plotted on the horizontal axis and the output values are plotted on the vertical axis. The graph of a function should have a specific shape and properties that define it as a function. Let’s examine the four given graphs to determine which one does not represent a function.
Graph A appears to be a straight line passing through the origin. This suggests that it represents a linear function, which is a type of function where the relationship between the input and output values is constant. Therefore, Graph A is a function.
Graph B is a parabola opening upwards. This shape indicates that it represents a quadratic function, which is another type of function where the relationship between the input and output values is not constant. Hence, Graph B is also a function.
Graph C is a horizontal line passing through the point (2, 3). This suggests that it represents a constant function, where the output value remains the same regardless of the input value. Therefore, Graph C is a function.
Now, let’s focus on Graph D. This graph consists of two separate lines, one passing through the origin and the other passing through the point (2, 3). This indicates that there are multiple output values for a single input value, which violates the definition of a function. Therefore, Graph D is not a function.
In conclusion, among the given graphs, Graph D is the one that does not represent a function. Understanding the characteristics of functions and their graphical representations is crucial in mathematics, as it helps us analyze and solve various problems involving relationships between input and output values.
