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 Discussion: All Topics Topic: confused Related Item: http://mathforum.org/mathtools/tool/15231/

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 Subject: RE: confused Author: proofpad Date: Jan 4 2005
On Jan  4 2005, satellite73j wrote:
> 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 y-axis).  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