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Topic:  confused 
Related Item:  http://mathforum.org/mathtools/tool/15231/ 
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Subject:  RE: confused 
Author:  proofpad 
Date:  Jan 4 2005 
> my students are often confused by this, and i can see why.
f(1)
> is not a point in the plane. if the graph is y = f(x) then of course
> f(1) is a point on the y axis. this applet will surely add to their
> confusion.
Unless I too am confused by the above, f(1) should be just a number and y = f(1)
is a point (on the plane, usually, not just the yaxis). Point out to
students (if this is the case) that f(1) is just evaluating an expression, and
when you evaluate, you get a number, not a point. Then tell them that f(1) = y
is an equation and that equations have solutions that can be graphed on either
number lines or planes (in this case, if f is a function, the point would in the
plane would be (1, f(1)) of course).
In other words, it boils down to the difference between an equation and an
expression, something I try to stress after seeing mentor teachers stress it to
their students.
Gabriel Edge
 
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