*This preview shows
page 1. Sign up
to
view the full content.*

**Unformatted text preview: **shall see in the next example that order is generally important when applying more than one transformation
to a graph.
3
We could equally have chosen the convention ‘outputs ﬁrst’. 1.8 Transformations 89 Since m(x) = f (x + 3) − 2 and f (x + 3) = m1 (x), we have m(x) = m1 (x) − 2. We can apply
Theorem 1.2 and obtain the graph of m by subtracting 2 from the y -coordinates of each of
the points on the graph of m1 (x). The graph veriﬁes that the domain of m is [−3, ∞) and
we ﬁnd the range of m is [−2, ∞). y y
(1, 2)
2 2 1 (−2, 1) 1 (1, 0) (−3, 0)
−3 −2 −1
−1 1 2 3 4 x −3 −2 −1
−1
(−2, −1) 2 3 4 x −2 −2 shift down 2 units y = m1 (x) = f (x + 3) = 1 √ −− − − − −→
−−−−−−
x+3 subtract 2 from each y -coordinate (−3, −2)
y = m(x) = m1 (x) − 2 = √ x+3−2 Keep in mind that we can check our answer to any of these kinds of problems by showing that any
of the points we’ve moved lie on the graph of our ﬁnal answer. For example, we can check that...

View
Full
Document