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If a vertical line intersects the graph of a relation at exactly one point, it implies that a single [latex]x[/latex]-value is only paired to a unique value of [latex]y[/latex]. On the other hand, if the vertical line intersects the graph more than once, this suggests that a single [latex]x[/latex]-value is being associated with more than one ...
Nov 11, 2022 · Step One: Observe the given graph and draw one or multiple vertical lines through the graph. Step Two: Note how many times the vertical line (s) that you drew intersected the graph (either coordinate points or a line/curve). Step Three: Based on the number of intersections, determine whether or not the relation is a function.
Figure \(\PageIndex{10}\): Graph of a polynomial. The vertical line test can be used to determine whether a graph represents a function. If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because a function has only one output value for each input value. See Figure \(\PageIndex{11}\).
The vertical line test works because to be a function, each x-value must lead to a single y-value. A vertical line is constant in x but varies in y, so if it only intersects once with the graph then the x-value leads to a unique y-value. Two Types of Function. If different x-values are associated to the same y-value, this is called a many-to ...
Once we have determined that a graph defines a function, an easy way to determine if it is a one-to-one function is to use the horizontal line test. Draw horizontal lines through the graph. If any horizontal line intersects the graph more than once, then the graph does not represent a one-to-one function.
If any vertical line intersects a graph more than once, the relation represented by the graph is not a function. Notice that any vertical line would pass through only one point of the two graphs shown in parts (a) and (b) of Figure 9. From this we can conclude that these two graphs represent functions.
Feb 1, 2024 · A function is a special relationship where every input in the domain has exactly one output in the range. To check if a graph is a function, I use the vertical line test. This method involves imagining drawing vertical lines through every part of the graph. If any vertical line intersects the graph at more than one point, then it’s not a ...
