Answer:
In this section, we study how the graphs of functions change, or transform, when certain specialized
modifications are made to their formulas. The transformations we will study fall into three broad
categories: shifts, reflections and scalings, and we will present them in that order. Suppose the
graph below is the complete graph of a function f.
(0, 1)
(2, 3)
(4, 3)
(5, 5)
x
y
1 2 3 4 5
2
3
4
5
y = f(x)
The Fundamental Graphing Principle for Functions says that for a point (a, b) to be on the graph,
f(a) = b. In particular, we know f(0) = 1, f(2) = 3, f(4) = 3 and f(5) = 5. Suppose we wanted to
graph the function defined by the formula g(x) = f(x) + 2. Let’s take a minute to remind ourselves
of what g is doing. We start with an input x to the function f and we obtain the output f(x).
The function g takes the output f(x) and adds 2 to it. In order to graph g, we need to graph the
points (x, g(x)). How are we to find the values for g(x) without a formula for f(x)? The answer is
that we don’t need a formula for f(x), we just need the values of f(x). The values of f(x) are the
y values on the graph of y = f(x). For example, using the points indicated on the graph of f, we
Step-by-step explanation:
