Need help with a graphing problem.
- Thread starter DawnK
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mmm4444bot
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Maybe you need to review some concepts.
Does the name Horizontal Line Test or the phrase "one-to-one function" ring any bells? If you can draw a horizontal line anywhere that intersects the graph in more than one place, then the test fails. This shows that the function values are not continually increasing (or continually decreasing) -- in other words, some y-values are repeated so there is no one-to-one correspondence between x and y values on the graph.
In order for a function to have an inverse, its graph must pass the Horizontal Line Test because only functions with one-to-one behavior have inverses.
If a function's graph shows that the function is not one-to-one (i.e., either not continually increasing OR not continually decreasing), then the domain must be restricted to some place where the graph does pass the Horizontal Line Test.
Examine a graph of your given function (x from -3 to 3 and y from -5 to 5 should be good enough), and then apply the given restrictions to see which yields a graph that passes the Horizontal Line Test.
Here are some Google results to check out, if you're interested. Cheers :cool:
Does the name Horizontal Line Test or the phrase "one-to-one function" ring any bells? If you can draw a horizontal line anywhere that intersects the graph in more than one place, then the test fails. This shows that the function values are not continually increasing (or continually decreasing) -- in other words, some y-values are repeated so there is no one-to-one correspondence between x and y values on the graph.
In order for a function to have an inverse, its graph must pass the Horizontal Line Test because only functions with one-to-one behavior have inverses.
If a function's graph shows that the function is not one-to-one (i.e., either not continually increasing OR not continually decreasing), then the domain must be restricted to some place where the graph does pass the Horizontal Line Test.
Examine a graph of your given function (x from -3 to 3 and y from -5 to 5 should be good enough), and then apply the given restrictions to see which yields a graph that passes the Horizontal Line Test.
Here are some Google results to check out, if you're interested. Cheers :cool:
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