Answer:
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
can make the following table.
x (x, f(x)) f(x) g(x) = f(x)
In general, if (a, b) is on the graph of y = f(x), then f(a) = b, so g(a) = f(a) + 2 = b + 2. Hence,
(a, b+ 2) is on the graph o
main role x (x, f(x)) f(x) g(x) = f(x) + 2 (x, g(x))
0 (0, 1) 1 3 (0, 3)
2 (2, 3) 3 5 (2, 5)
4 (4, 3) 3 5 (4, 5)
5 (5, 5) 5 7 (5, 7)
Step-by-step explanation:
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