1, 2
(
)
f f( 1)= 2
x=2 y 2.8 f(2) 2.8
f(x)=2 y=2 y=2 x= 3 x=1
x y=0 x= 2.5 x=0.3
f x f
3 x 3 3,3 f y f
2 y 3 2,3
x 1 3 y 2 3 f 1,3
4, 2
(
)
f f( 4)= 2 3,4
(
)
g
g(3)=4
x y y f g
2,1
(
)
2,2
(
)
x 2 2
f(x)= 1 y= 1 y= 1 x= 3 x=4
x 0 4 y 3 1 f 0,4
f x f
4 x 4 4,4 f y f
2 y 3 2,3
g 4,3 0.5,4
t,a
(
)
= 12, 85
(
)
17,115
(
)
85 a 115
325 a 485
210 a 200
60 / 2 d
t t|0 t 2
{
}
t
d|0 d 120
{
}
d
N
t t|0 t 24
{
}
t
N|0 N k
{
}
N k
1. (a) The point is on the graph of , so .
(b) When , is about , so .
(c)
is equivalent to . When , we have and .
(d) Reasonable estimates for when are and .
(e) The domain of
consists of all values on the graph of . For this function, the domain is
, or . The range of consists of all values on the graph of . For this function,
the range is , or .
(f) As
increases from to , increases from to . Thus, is increasing on the interval
.
2. (a) The point
is on the graph of , so . The point is on the graph of , so
.
(b) We are looking for the values of
for which the values are equal. The values for and
are equal at the points and , so the desired values of are and .
(c) is equivalent to . When , we have and .
(d) As increases from to , decreases from to . Thus, is decreasing on the interval
.
(e) The domain of
consists of all values on the graph of . For this function, the domain is
, or . The range of consists of all values on the graph of . For this function,
the range is
, or .
(f) The domain of is and the range is .
3. From Figure 1 in the text, the lowest point occurs at about
. The highest point
occurs at about
. Thus, the range of the vertical ground acceleration is . In
Figure 11, the range of the north
south acceleration is approximately . In Figure 12,
the range of the east
west acceleration is approximately .
4. Example 1: A car is driven at
mi h for hours. The distance traveled by the car is a function
of the time . The domain of the function is , where is measured in hours. The range of
the function is , where is measured in miles.
Example 2: At a certain university, the number of students on campus at any time on a particular
day is a function of the time
after midnight. The domain of the function is , where is
measured in hours. The range of the function is , where is an integer and is the
largest number of students on campus at once.
1
Stewart Calculus ET 5e 0534393217;1. Functions and Models; 1.1 Four Ways to Represent a Function
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