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Unformatted text preview: g and f in the last example, we notice that to
obtain the graph of f from the graph of g , we reﬂect a portion of the graph of g about the x-axis.
We can see this analytically by substituting g (x) = x2 − x − 6 into the formula for f (x) and calling
to mind Theorem 1.4 from Section 1.8.
f (x) = −g (x), if g (x) < 0
g (x), if g (x) ≥ 0 The function f is deﬁned so that when g (x) is negative (i.e., when its graph is below the x-axis),
the graph of f is its refection across the x-axis. This is a general template to graph functions
of the form f (x) = |g (x)|. From this perspective, the graph of f (x) = |x| can be obtained by
reﬂection the portion of the line g (x) = x which is below the x-axis back above the x-axis creating
the characteristic ‘∨’ shape. 148 2.3.1 Linear and Quadratic Functions Exercises 1. Graph each of the following quadratic functions. Find the x- and y -intercepts of each graph,
if any exist. If it is given in the general form, convert it into standard form. Find the
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