SOLUTION: Determine if the graph is a graph of a one-to-one function.
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Question 1198312: Determine if the graph is a graph of a one-to-one function.
Found 3 solutions by greenestamps, math_tutor2020, ikleyn:
Answer by greenestamps(13215) (Show Source): You can put this solution on YOUR website!
No graph is shown....
Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!
No graph is shown, which makes it impossible to answer your current question.
However, I'll give two examples to help get you started.
The graph of is NOT one-to-one because it fails the horizontal line test
Notice how it's possible to draw a single horizontal line through more than one point on the blue curve.
One such example is a horizontal line through 1 on the y axis intersecting the blue curve at (-1,1) and (1,1).
This is visual evidence of the curve failing the horizontal line test.
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In contrast, the graph of is one-to-one because it passes the horizontal line test.
It is impossible to draw a single horizontal line through more than one point on the green curve below.
Answer by ikleyn(52908) (Show Source): You can put this solution on YOUR website!
.
In school mathematics, all functions are continuous (well, if not all, then 99.99% of functions are continuous).
For continuous functions defined on the entire number line or on it parts (like a segment),
the given function (the continuous function) is one-to-one if and only if it is monotonic.
It is the major fact which you need to know about the subject in the school.
In the university, if you will learn Math as your major, you, probably, will be acquainted
with other interesting one-to-one functions, that are not continuous.
Probably, then you will learn there other examples of discontinuous functions,
that are still one-to-one, but for school, what I explained in my post is more than enough.
So, in the school, if they ask you if the given function is one-to-one,
your first step is to check if the function is monotonic on the entire number line
or on some its interval/segment.
It will provide you the answer to the question.
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