for Physics 50 series
an 8-page guide to concepts important for these courses.
By Todd Sauke
We start with the important concept of a
A function is a mathematical
relation for which, if given an input value (the
"argument"), the result (the "output" value of
the function for that argument) is given by
exactly one number.
In the same way that we
can refer generally to an arbitrary or unknown
quantity as "x", we can refer generally to some
arbitrary or unknown function using an
abstraction like "F(x)".
A function can be
thought of as a mathematical
") that produces a single output number
for any input number in the domain of the
The specific relation, F(x) = x
is a function; for
value of the input, x,
you can compute
F(3) = 3
+ 1 = 10, for example.
value of a function is also called an
square root of x) is
a function, since the
result, for example, for x=4 gives
possible results, rather than
A function can be plotted
as a graph showing a curve of
long as there is exactly one and only one value
corresponding to each input value. We can
also have functions with
(or multiple independent variables), say a
function of x, y, and z such that there is
exactly one output result for any combination
of input values x, y and z.
For example, F(x, y, z) = 3 + 2xy
function of x, y and z.
For x=1, y=3 and z=2,
F(1, 3, 2) = 3 + 18 – 16 = 5,
output number corresponding to the specific
Sometimes a curve on a graph,
say the circle in the x,y plane given by the
, does not represent a
However, this same curve
could be considered a function r(
In that case, each value of