4
Chapter 1: Functions
To ﬁnd out, we could plot more points. But how would we then connect them? The basic
question still remains: How do we know for sure what the graph looks like between the
points we plot? Calculus answers this question, as we will se
14
Chapter 1: Functions
1 .2 Combining Functions; Shifting and Scaling Graphs
In this section we look at the main ways functions are combined or transformed to form
new functions.
Sums, Differences, Products, and Quotients
Like numbers, functions can be a
24 Chapter 1: Functions
Periodicity and Graphs of the Trigonometric Functions
When an angle of measure 6 and an angle of measure 6 + 211' are in standard position,
their terminal rays coincide. The two angles therefore have the same trigonometric func—
ti
34 Chapter 1: Functions
Solution Using regression software that allows us to ﬁt a straight line as well as a qua-
TABLE 1.4 U.S. deaths from dratic curve, we enter the data to obtain the formulas
I .
tUbem” 05's y = 222791-105 i 111.04x, line ﬁt
Yea
44 Chapter 1: Functions
.3’ y=2.x—2
FIGURE 1.60 Graphing
f(x) = (1/2)x + l and f‘l(x) = 2x — 2
together shows the graphs’ symmetry with
respect to the line y = x (Example 3).
FIGURE 1.61 The functions y = V;
2
and y : x ,x 2 0. are inverses of one
ano
54
Chapter 1: Functions
Chapter" Questions to Guide Your Review
10.
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14.
. What is a function? What is its domain? Its range? What is an
arrow diagram for a function? Give examples.
. What is the graph of a real—valued function of a real variab