Mate V (Funciones)

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CHAPTER 1 FUNCTIONS AND MODELS

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(a) (b) (c) (d) (e) (f)

Exercises
5–8 |||| Determine whether the curve is the graph of a function of x. If it is, state the domain and range of the function.

1. The graph of a function f is given.

State the value of f 1 . Estimate the value of f 2 . For what values of x is f x 2? Estimate the values of x such that f x State thedomain and range of f. On what interval is f increasing?
y

5.

y 1 0 1 x

6.

y 1 0 1 x

0.

7.
1

y
1

8.

y 1

0

1

x

0

1

x

0

1

x

s

s

s

s

s

s

s

s

s

s

s

s

2. The graphs of f and t are given. (a) State the values of f 4 and t 3 . (b) For what values of x is f x tx? (c) Estimate the solution of the equation f x (d)On what interval is f decreasing? (e) State the domain and range of f. (f) State the domain and range of t.
y

9. The graph shown gives the weight of a certain person as a

1.

function of age. Describe in words how this person’s weight varies over time. What do you think happened when this person was 30 years old?

200 Weight (pounds) 150 100 50

g f
2

0
0 2 x

10

20 30 4050

60 70

Age (years)

10. The graph shown gives a salesman’s distance from his home as

a function of time on a certain day. Describe in words what the graph indicates about his travels on this day.
3. Figures 1, 11, and 12 were recorded by an instrument operated

by the California Department of Mines and Geology at the University Hospital of the University of Southern California inLos Angeles. Use them to estimate the ranges of the vertical, north-south, and east-west ground acceleration functions at USC during the Northridge earthquake.
4. In this section we discussed examples of ordinary, everyday

Distance from home (miles)

8 A.M.

10

NOON

2

4

6 P.M.

Time (hours)

functions: Population is a function of time, postage cost is a function of weight,water temperature is a function of time. Give three other examples of functions from everyday life that are described verbally. What can you say about the domain and range of each of your functions? If possible, sketch a rough graph of each function.

11. You put some ice cubes in a glass, fill the glass with cold

water, and then let the glass sit on a table. Describe how the temperature ofthe water changes as time passes. Then sketch a rough graph of the temperature of the water as a function of the elapsed time.

SECTION 1.1 FOUR WAYS TO REPRESENT A FUNCTION

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23

12. Sketch a rough graph of the number of hours of daylight as a

23–27

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Find the domain of the function. x 3x st 1
4 sx 2
s s

function of the time of year.
13. Sketch a rough graph of theoutdoor temperature as a function 23. f x 25. f t 27. h x
s s

1 st 5x
s s

24. f x 26. t u

5x x2 su 3x

4 2 u

of time during a typical spring day.
14. You place a frozen pie in an oven and bake it for an hour. Then

3

s4

you take it out and let it cool before eating it. Describe how the temperature of the pie changes as time passes. Then sketch a rough graph of thetemperature of the pie as a function of time.
15. A homeowner mows the lawn every Wednesday afternoon.

s

s

s

s

s

s

Sketch a rough graph of the height of the grass as a function of time over the course of a four-week period.
16. An airplane flies from an airport and lands an hour later at

28. Find the domain and range and sketch the graph of the function

hx
29–40
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s4x 2.

Find the domain and sketch the graph of the function. 5 t2 sx 3x x x x 1 if x if x if x if x 1 1 0 0 1 1 6t 5 x
30. F x 32. H t 34. F x 36. t x
1 2

another airport, 400 miles away. If t represents the time in minutes since the plane has left the terminal building, let x t be the horizontal distance traveled and y t be the altitude of the plane. (a) Sketch a possible graph of x t ....