Unformatted text preview: (1, 0) and (10, 1), along with the vertical asymptote
x = 0. Since f (x) = 2h(−x + 3) − 1, Theorem 1.7 tells us that to obtain the destinations of
these points, we ﬁrst subtract 3 from the x-coordinates (shifting the graph left 3 units), then
divide (multiply) by the x-coordinates by −1 (causing a reﬂection across the y -axis). These
transformations apply to the vertical asymptote x = 0 as well. Subtracting 3 gives us x = −3
as our asymptote, then multplying by −1 gives us the vertical asymptote x = 3. Next, we
multiply the y -coordinates by 2 which results in a vertical stretch by a factor of 2, then we
ﬁnish by subtracting 1 from the y -coordinates which shifts the graph down 1 unit. We leave
it to the reader to perform the indicated arithmetic on the points themselves and to verify
the graph produced by the calculator below.
2. To ﬁnd the domain of g , we set x−1 > 0 and use a sign diagram to solve this inequality. We
deﬁne r(x) = x−1 ﬁnd its domain t...
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