Chapter Sixteen — Graphing Functions
The Humongous Book of Algebra Problems
graph of r(x) is (–4,5), and any horizontal line below (and including) y = 5
intersects the graph. This is even true for y = 2. Although the graph excludes
point (1,2), the horizontal line y = 2 passes through the graph of r(x) at two
other points. Therefore, the range is r(x) ≤ 5.
Pieces of a graph are reections of each other
16.21 Complete the graph of f(x) in Figure 16-8 assuming it is y-symmetric.
Figure 16-8: A portion of the graph of f(x).
A y-symmetric function is a reﬂection of itself across the y-axis, so if the graph
passes through point (x,y), it passes through the corresponding point (–x,y) as
well. For instance, the graph of f(x) in Figure 16-8 passes through point (4,–3),
so it must pass through (–4,–3) as well. Figure 16-9 presents the completed
graph of f(x).
graphed f(x) on
a sheet of paper
and folded the paper
along the y-axis, the
left and right sides
of f(x) would