Hello!
The y-intercept of a function is the point of intersection of the graph of this function and the y-axis. So such a point belongs both to y-axis and to the graph of a function.
All points on the y-axis have an x-coordinate of 0, they are of the form where
may be any number.
All points on the graph of a function have the form
where
is any number from the domain of
If both conditions are met, we have and the second coordinate is
hence the y-intercept of
is the point
it is unique if function is one-valued. Of course this requires that
is in the domain of
otherwise
has no y-intercept.
For example, has the y-intercept
and
has no y-intercept.
More general curves, not graphs of (one-valued) functions, may have more than one y-intercept, for example the circle has two (find them yourself using
).
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