Question

On a sheet of graph paper, create two graphs. Your first graph must represent a function, and the second graph must not represent a function. Explain how you know which graph is a function. Graph paper can be printed from the resources tab of this lesson.

Answer 1

To determine if a graph represents a function, you need to check if each input value has only one corresponding output value. If so, it is a function. If there are multiple output values for a single input value, it is not a function.

Step-by-step explanation:

To create a graph that represents a function, you will need to make sure that for every input value (x-coordinate), there is only one output value (y-coordinate). This means that a vertical line drawn on the graph should intersect the graph at most once. For example, the graph of the equation y = 2x + 1 represents a function because each value of x corresponds to a unique value of y.

On the other hand, a graph that does not represent a function will have a vertical line that intersects the graph at more than one point. This means that there are multiple output values for a single input value. For example, the graph of a circle does not represent a function because a vertical line can intersect the circle at two points.

By examining the relationship between the input and output values on the graph, you can determine whether it represents a function or not.