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Stitz-Zeager_College_Algebra_e-book

# 7 when interpreting rates of change we interpret them

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Unformatted text preview: s the graph of the line y = 3x − 1. Comparison of this equation with Equation 2.3 yields m = 3 and b = −1. Hence, our slope is 3 and our y -intercept is (0, −1). To get another point on the line, we can plot (1, f (1)) = (1, 2). y 4 y 3 2 4 1 3 −2 −1 −1 2 1 2 x −2 1 −3 −4 −3 −2 −1 1 f (x) = 3 2 3 x f (x) = 3x − 1 2.1 Linear Functions 117 3. At ﬁrst glance, the function f (x) = 3−2x does not ﬁt the form in Deﬁnition 2.1 but after some 4 x 3 rearranging we get f (x) = 3−2x = 3 − 24 = − 1 x + 4 . We identify m = − 1 and b = 3 . Hence, 4 4 2 2 4 1 our graph is a line with a slope of − 2 and a y -intercept of 0, 3 . Plotting an additional 4 point, we can choose (1, f (1)) to get 1, 1 . 4 4. If we simplify the expression for f , we get f (x) = \$ x2 − 4 \$\$\$ x + 2) (x − 2)( = x + 2. = \$ (x − 2) x−2 \$\$\$ If we were to state f (x) = x + 2, we would be committing a sin of omission. Remember, to ﬁnd the domain of a function, we do so before we simplify! In this case, f has big problems when x = 2, and as such, the...
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