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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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