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

**Unformatted text preview: **have 39 ≤ S (x) ≤ 45.
Using absolute value and the fact that S (x) = 6x2 we get |6x2 − 42| ≤ 3. Solving this inequality
13
15
,
.
yields
2
2
6. (a) (b) y y 3 4 2 3 1
−2 −1 2
1 2 3 1 x −1
−2
−3 −2 −1 1 2 x 2.4 Inequalities 169 (c) (e) y y 5 4 4 3 3 2 2 1 1
−2 −1
−2 −1 1 x 2 1 2 3 x 1 2 −1
−2
−3 (d) −4 y
4 (f) 3
2 20 1 15
10 −1 1 2 x 5
−4 −3 −2 −1 3 170 2.5 Linear and Quadratic Functions Regression In this section, we use some basic tools from statistical analysis to quantify linear and quadratic
trends that we may see in data. Our goal is to give the reader an understanding of the basic processes
involved, but we are quick to refer the reader to a more advanced course1 for a complete exposition
of this material. Suppose we collected three data points, {(1, 2), (3, 1), (4, 3)}. By plotting these
points, we can clearly see they do not lie along the same line. If we pick any two of the points,
we can ﬁnd a line containing both which completely misses the third, but our ai...

View
Full
Document