Unformatted text preview: in 1 to graph m(x) = x + 3 − 2.
1. Graph f (x) = Solution.
1. Owing to the square root, the domain of f is x ≥ 0, or [0, ∞). We choose perfect squares to
build our table and graph below. From the graph we verify the domain of f is [0, ∞) and the
range of f is also [0, ∞).
y x
0
1
4 f (x) (x, f (x))
0
(0, 0)
1
(1, 1)
2
(4, 2) (4, 2)
2 (1, 1)
1 (0, 0)
1 2 y = f (x) = 3 √ 4 x x 2. The domain of g is the same as the domain of f , since the only condition on both functions
is that x ≥ 0. If we compare the formula for g (x) with f (x), we see that g (x) = f (x) − 1.
In other words, we have subtracted 1 from the output of the function f . By Theorem 1.2,
we know that in order to graph g , we shift the graph of f down one unit by subtracting
1 from each of the y coordinates of the points on the graph of f . Applying this to the three
points we have speciﬁed on the graph, we move (0, 0) to (0, −1), (1, 1) to (1, 0), and (4, 2) to
(4, 1). The rest of the points follow suit, and we connect them with the same basic shape as
before. We con...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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