How Do Functions Function?
Functions are one of the most important additions to the
Math section of the new SAT. So, what’s a function? A function describes
a relationship between one or more inputs and one output. The inputs
to a function are variables such as x;
the output of the function for a particular value of x is
usually represented as f(x) or g(x).
In the function f(x) = 2x,
the output of the function is always equal to two times the value of x.
So, if x = 1, then f(x)
= 2, and if x = 12, then f(x)
So far, it may seem as if a function is
just another word for equation. Based on the way
the SAT generally tests functions, it’s fine to think of functions
that way. However, all functions follow a special rule that you’ve
got to know:
For every input x,
a function can have only one value for f(x).
You might be asking yourself what this math babble means.
Here’s an example that should help translate. Take the equation |y|
= x. Because y sits
between absolute value brackets, if x = 2,
then y could be equal to either 2 or –2.
This equation can’t be a function, because for each value of x,
there are two possible values of y.