Functions and Equations
The concept of functions is fundamental to mathematics. A function
expresses the relationship between two (or more) terms called variables,
and is typically written in the form of an equation (an algebraic expression
set equal to another algebraic expression). Variables are named as such
because, as the name implies, their values may vary. Variables are usually
expressed with letters of the alphabet. The two most common variables you
will see used in mathematical equations are x and y (although any letter or
symbol is just as valid).
If each value of x can be associated with one value of y, then y is a func

tion of x. y is said to be the dependent variable since its value depends on
the value of x. Here are a couple of examples:
(1.1)
(1.2)
In the second example, the m and the c represent constants (sometimes
called coefficients) — values that never change no matter what the value
of x is. They are effectively similar to the 2 in equation (1.1). Therefore, if
a = 2, equation (1.1) can be written as follows:
(1.3)
Given any value of x, the corresponding y value can be calculated by put
ting the x value into the function. Given x = 5 and x = 7 and the function
y =2x, the y values are:
(1.4)
This type of function, where y is only dependent on one other variable, is
called a singlevariable function. Singlevariable functions may be visual

ized by plotting them onto the xy Cartesian plane. To plot a function, all
you have to do is move along the xaxis and for each x value use the func

tion to calculate the y value. Of course, it’s impossible to plot the graph for
every value of x — that would take forever (literally) — so you must select
a range of values.
The lefthand side of Figure 1.3 shows how function y =2x looks when
plotted on the xy plane, using the range of x values between –5.0 and 5.0.
A Math and Physics Primer  3
Mathematics
2yx=
ymxc=+
yax=
2(5) 10
2(7) 14
y
y
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