2. y x² + 1 %3D V3 0. V3 2. -2 V3 -1 - V3 -2 4x x2 + 1 FIGURE 13.63 Graph of y 4.x/(x² + 1) is given in Figure 13.63, together with a table of important points. Now Work Problem 39 %3D Discussion After consideration of all of the preceding information, the graph of y PROBLEMS 13.5 In Problems 1–24, find the vertical asymptotes and the nonvertical asymptotes for the graphs of the functions. Do not sketch the graphs. nonvertical asymptotes; and those intercepts that can be obtained conveniently. Then sketch the curve. 3 25. y= 2. 2x - 3 26. y = - 1. y= 28. y= x - 1 Ds. 27. y = X - 1 2x + 1 = (x)f £ 2x + 7 4. y= 3x2 – 5x – 1 2x + 1 29. y = x² + 30. y = %3D 4. 5. y = 6. y = 1 – x2 - 31. y= マ-1 %3D 32. y= x² + 1 %3D 7. y = x² – 1 I-さ- 8. y = 34. y = x2 33. y= x+ %3D on 9. y = x – 5x +52) n 10. y = x3 – 4 | bianoototal %3D 36. y= 35. y = 7x+4 %3D 2x2 = (x)f 5. 4x2 + 2x + 1 6. 9x2 – 6x – 8 3x + 1 11. f(x) = %3D 38. y = %3D 37. y = 2r2 3x + 1 %3D %3D 9 -x+ z* 2x³ + 1 | 15x2 + 31x + 1 13. y = x2 - 7 14. y= 3x(2x – 1)(4x – 3) 39. y = 40. y = - (6x + 5)2 (3x – 2)2 x² - 1 %3D 2 = (x)f *91 2x2 - 9x +4 5x² + 7x³ + 9x 15. y=マ-3 +5 42. y = %3D 41. y= (x – 2)2 3x4 + 1 x - 3 %3D | 3 – x4 1. 43. y = 2x +1+ 17. f(x) 18. y = 3x2 44. y = %3D x³ + x² x² – 3x - 4 x* +1 -3x2 + 2x – 5 19. y= 20. y= 1 – x4 45. y = 46. y = 3x + 2+ 1+4x + 4x² 3x2 - 2x 1 3x + 2 2. 22. y = 47. Sketch the graph of a function f such that f (0) = 0, there is a horizontal asymptote y = 1 for x → ±oo, there is a vertical asymptote x = 2, both f'(x) < 0 and f"(x) < 0 for x < 2, and both f'(x) < 0 and f"(x) > 0 for x > 2. 9x2 – 16 - %3D 21. y = 12x2 + 5x – 2 5. 24. f(x) = 12e-r 2(3x + 4)2 %3D 23. y = 5e-3 - 2 %3D In Problems 25-46, determine intervals on which the function is increasing, decreasing, concave up, and concave down; relative maxima and minima; inflection points; symmetry; vertical and 48. Sketch the graph of a function f such that f (0) = -4 and f(4) = -2, there is a horizontal asymptote y = -3 for x→ ±, %3D
2. y x² + 1 %3D V3 0. V3 2. -2 V3 -1 - V3 -2 4x x2 + 1 FIGURE 13.63 Graph of y 4.x/(x² + 1) is given in Figure 13.63, together with a table of important points. Now Work Problem 39 %3D Discussion After consideration of all of the preceding information, the graph of y PROBLEMS 13.5 In Problems 1–24, find the vertical asymptotes and the nonvertical asymptotes for the graphs of the functions. Do not sketch the graphs. nonvertical asymptotes; and those intercepts that can be obtained conveniently. Then sketch the curve. 3 25. y= 2. 2x - 3 26. y = - 1. y= 28. y= x - 1 Ds. 27. y = X - 1 2x + 1 = (x)f £ 2x + 7 4. y= 3x2 – 5x – 1 2x + 1 29. y = x² + 30. y = %3D 4. 5. y = 6. y = 1 – x2 - 31. y= マ-1 %3D 32. y= x² + 1 %3D 7. y = x² – 1 I-さ- 8. y = 34. y = x2 33. y= x+ %3D on 9. y = x – 5x +52) n 10. y = x3 – 4 | bianoototal %3D 36. y= 35. y = 7x+4 %3D 2x2 = (x)f 5. 4x2 + 2x + 1 6. 9x2 – 6x – 8 3x + 1 11. f(x) = %3D 38. y = %3D 37. y = 2r2 3x + 1 %3D %3D 9 -x+ z* 2x³ + 1 | 15x2 + 31x + 1 13. y = x2 - 7 14. y= 3x(2x – 1)(4x – 3) 39. y = 40. y = - (6x + 5)2 (3x – 2)2 x² - 1 %3D 2 = (x)f *91 2x2 - 9x +4 5x² + 7x³ + 9x 15. y=マ-3 +5 42. y = %3D 41. y= (x – 2)2 3x4 + 1 x - 3 %3D | 3 – x4 1. 43. y = 2x +1+ 17. f(x) 18. y = 3x2 44. y = %3D x³ + x² x² – 3x - 4 x* +1 -3x2 + 2x – 5 19. y= 20. y= 1 – x4 45. y = 46. y = 3x + 2+ 1+4x + 4x² 3x2 - 2x 1 3x + 2 2. 22. y = 47. Sketch the graph of a function f such that f (0) = 0, there is a horizontal asymptote y = 1 for x → ±oo, there is a vertical asymptote x = 2, both f'(x) < 0 and f"(x) < 0 for x < 2, and both f'(x) < 0 and f"(x) > 0 for x > 2. 9x2 – 16 - %3D 21. y = 12x2 + 5x – 2 5. 24. f(x) = 12e-r 2(3x + 4)2 %3D 23. y = 5e-3 - 2 %3D In Problems 25-46, determine intervals on which the function is increasing, decreasing, concave up, and concave down; relative maxima and minima; inflection points; symmetry; vertical and 48. Sketch the graph of a function f such that f (0) = -4 and f(4) = -2, there is a horizontal asymptote y = -3 for x→ ±, %3D
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
Related questions
Question
31 and 35
Transcribed Image Text:2.
y
x² + 1
%3D
V3
0.
V3
2.
-2
V3
-1
- V3
-2
4x
x2 + 1
FIGURE 13.63 Graph of y
4.x/(x² + 1) is given in Figure 13.63, together with a table of important points.
Now Work Problem 39
%3D
Discussion After consideration of all of the preceding information, the graph of y
PROBLEMS 13.5
In Problems 1–24, find the vertical asymptotes and the nonvertical
asymptotes for the graphs of the functions. Do not sketch the
graphs.
nonvertical asymptotes; and those intercepts that can be obtained
conveniently. Then sketch the curve.
3
25. y=
2.
2x - 3
26. y =
-
1. y=
28. y=
x - 1
Ds.
27. y =
X - 1
2x + 1
= (x)f £
2x + 7
4. y=
3x2 – 5x – 1
2x + 1
29. y = x² +
30. y =
%3D
4.
5. y =
6. y = 1 –
x2
-
31. y= マ-1
%3D
32. y=
x² + 1
%3D
7. y =
x² – 1
I-さ-
8. y =
34. y =
x2
33. y=
x+
%3D
on
9. y = x – 5x +52) n 10. y =
x3 – 4
|
bianoototal
%3D
36. y=
35. y = 7x+4
%3D
2x2
= (x)f
5.
4x2 + 2x + 1
6.
9x2 – 6x – 8
3x + 1
11. f(x) =
%3D
38. y =
%3D
37. y =
2r2
3x + 1
%3D
%3D
9 -x+ z*
2x³ + 1
|
15x2 + 31x + 1
13. y =
x2 - 7
14. y=
3x(2x – 1)(4x – 3)
39. y =
40. y =
-
(6x + 5)2
(3x – 2)2
x² - 1
%3D
2
= (x)f *91
2x2 - 9x +4
5x² + 7x³ + 9x
15. y=マ-3
+5
42. y =
%3D
41. y=
(x – 2)2
3x4 + 1
x - 3
%3D
|
3 – x4
1.
43. y = 2x +1+
17. f(x)
18. y =
3x2
44. y =
%3D
x³ + x²
x² – 3x - 4
x* +1
-3x2 + 2x – 5
19. y=
20. y=
1 – x4
45. y =
46. y = 3x + 2+
1+4x + 4x²
3x2 - 2x 1
3x + 2
2.
22. y =
47. Sketch the graph of a function f such that f (0) = 0, there
is a horizontal asymptote y = 1 for x → ±oo, there is a vertical
asymptote x = 2, both f'(x) < 0 and f"(x) < 0 for x < 2, and both
f'(x) < 0 and f"(x) > 0 for x > 2.
9x2 – 16
-
%3D
21. y =
12x2 + 5x – 2
5.
24. f(x) = 12e-r
2(3x + 4)2
%3D
23. y = 5e-3 - 2
%3D
In Problems 25-46, determine intervals on which the function is
increasing, decreasing, concave up, and concave down; relative
maxima and minima; inflection points; symmetry; vertical and
48. Sketch the graph of a function f such that f (0) = -4 and
f(4) = -2, there is a horizontal asymptote y = -3 for x→ ±,
%3D
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