Stitz-Zeager_College_Algebra_e-book

# Isolate the exponential function 2 a if convenient

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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. x 2. To ﬁnd the domain of g , we set x−1 > 0 and use a sign diagram to solve this inequality. We x deﬁne r(x) = x−1 ﬁnd its domain t...
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## This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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