Is the given graph a function?
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Is the given graph a function?
To determine if the given graph represents a function, we use the vertical line test: if any vertical line intersects the graph at more than one point, the graph is not a function.
Let's apply this test to the graph:
Upon examining the graph, we observe that there are several vertical lines that intersect the graph at multiple points, particularly in areas with loops or overlapping curves. This indicates that at those -values, there are multiple -values corresponding to them.
Since there exist such vertical lines, according to the vertical line test, the graph does not represent a function.
Thus, the solution to this problem is that the given graph is not a function.
No
Determine whether the following table represents a constant function:
You're looking for any vertical line that crosses the graph more than once. If you find even one such line, the graph fails the test and is not a function.
You don't need to check every possible line! Focus on areas where the graph curves back on itself, has loops, or appears to overlap. These are the most likely trouble spots.
Break it down into sections! Look for obvious loops, spirals, or places where the curve doubles back. Complex graphs often fail the vertical line test in multiple places.
Absolutely! Curves are fine as long as they don't loop back or overlap vertically. Think of - it's curved but still passes the vertical line test.
It means there are x-values with multiple y-values. In real life, this might represent a relationship where one input can produce different outputs - like a circle where one x-coordinate corresponds to two different heights.
Look for closed loops, figure-8 shapes, or any part that curves back over itself. These patterns almost always create multiple y-values for the same x-value.
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