Key Concepts [index]
A function F: A→ B is a relation that
assigns to each x ∈ A a unique y
∈ B. We write y = f(x) and call y the
value of f at x or the image of x under f. We also say
that f maps x to y.
The set A is called the domain of f. The set of all
possible values of f(x) in B is called the range of f.
Each of these transformations takes a function f and produces a new function g:
Horizontal translation: g(x) = f(x+c).
The graph is translated c units to the left if c > 0 and c units to the right if c < 0.
Vertical translation: g(x) = f(x)+k.
The graph is translated k units upward if k > 0 and k units downward if k < 0.
Change of amplitude: g(x) = Af(x) (A ≠ 0)
The amplitude of the graph is increased by a factor of A if
|A| > 1 and decreased by a factor of A if
|A| < 1. In addition, if A < 0
the graph is inverted.
Change of scale: g(x) = f(ax) (a ≠ 0)
The graph is ``compressed'' if |a| > 1 and ``stretched out'' if
|a| < 1. In addition, if a < 0 the graph is reflected
about the y-axis.