Search in book...
Toggle Font Controls
Create new playlist

Name your new playlist

Playlist description (optional)
Sign In

Email address

Password

Forgot Password?

or

Continue with Facebook

Continue with Google
Sign Up

Full Name

Email address

Confirm Email Address

Password

or

Continue with Facebook

Continue with Google

2.4 Exercise Set

Determine visually whether the graph is symmetric with respect to the x-axis, the y-axis, and the origin.

First, graph the equation and determine visually whether it is symmetric with respect to the x-axis, the y-axis, and the origin. Then verify your assertion algebraically.

7. $y = | x | - 2$ $y = | x | - 2$
8. $y = | x + 5 |$ $y = | x + 5 |$
9. $5 y = 4 x + 5$ $5 y = 4 x + 5$
10. $2 x - 5 = 3 y$ $2 x - 5 = 3 y$
11. $5 y = 2 x^{2} - 3$ $5 y = 2 x^{2} - 3$
12. $x^{2} + 4 = 3 y$ $x^{2} + 4 = 3 y$
13. $y = \frac{1}{x}$ $y = \frac{1}{x}$
14. $y = - \frac{4}{x}$ $y = - \frac{4}{x}$

Determine whether the graph is symmetric with respect to the x-axis, the y-axis, and the origin.

15. $5 x - 5 y = 0$ $5 x - 5 y = 0$
16. $6 x + 7 y = 0$ $6 x + 7 y = 0$
17. $3 x^{2} - 2 y^{2} = 3$ $3 x^{2} - 2 y^{2} = 3$
18. $5 y = 7 x^{2} - 2 x$ $5 y = 7 x^{2} - 2 x$
19. $y = | 2 x |$ $y = | 2 x |$
20. $y^{3} = 2 x^{2}$ $y^{3} = 2 x^{2}$
21. $2 x^{4} + 3 = y^{2}$ $2 x^{4} + 3 = y^{2}$
22. $2 y^{2} = 5 x^{2} + 12$ $2 y^{2} = 5 x^{2} + 12$
23. $3 y^{3} = 4 x^{3} + 2$ $3 y^{3} = 4 x^{3} + 2$
24. $3 x = | y |$ $3 x = | y |$
25. $x y = 12$ $x y = 12$
26. $x y - x^{2} = 3$ $x y - x^{2} = 3$

Find the point that is symmetric to the given point with respect to the x-axis, the y-axis, and the origin.

27. $(- 5, 6)$ $(- 5, 6)$
28. $(\frac{7}{2}, 0)$ $(\frac{7}{2}, 0)$
29. $(- 10, - 7)$ $(- 10, - 7)$
30. $(1, \frac{3}{8})$ $(1, \frac{3}{8})$
31. $(0, - 4)$ $(0, - 4)$
32. $(8, - 3)$ $(8, - 3)$

Determine visually whether the function is even, odd, or neither even nor odd.

Determine whether the function is even, odd, or neither even nor odd.

39. $f (x) = - 3 x^{3} + 2 x$ $f (x) = - 3 x^{3} + 2 x$
40. $f (x) = 7 x^{3} + 4 x - 2$ $f (x) = 7 x^{3} + 4 x - 2$
41. $f (x) = 5 x^{2} + 2 x^{4} - 1$ $f (x) = 5 x^{2} + 2 x^{4} - 1$
42. $f (x) = x + \frac{1}{x}$ $f (x) = x + \frac{1}{x}$
43. $f (x) = x^{17}$ $f (x) = x^{17}$
44. $f (x) = \sqrt[3]{x}$ $f (x) = \sqrt[3]{x}$
45. $f (x) = x - | x |$ $f (x) = x - | x |$
46. $f (x) = \frac{1}{x^{2}}$ $f (x) = \frac{1}{x^{2}}$
47. $f (x) = 8$ $f (x) = 8$
48. $f (x) = \sqrt{x^{2} + 1}$ $f (x) = \sqrt{x^{2} + 1}$

Skill Maintenance

49. Graph: $f (x) = {\begin{aligned} x - 2, & for x \leq - 1, \\ 3, & for - 1 < x \leq 2, \\ x, & for x > 2. \end{aligned}$ $f (x) = {\begin{aligned} x - 2, & for x \leq - 1, \\ 3, & for - 1 < x \leq 2, \\ x, & for x > 2. \end{aligned}$ [2.1]
50. Peace Corps Volunteers. Since 1961, there has been a total of 6688 Peace Corps volunteers from the University of California–Berkeley and the University of Wisconsin–Madison. The number of volunteers from the University of California–Berkeley is 464 more than the number of volunteers from the University of Wisconsin–Madison. (Source: Peace Corps 2014) Find the number of Peace Corps volunteers from each university. [1.5]

Synthesis

Determine whether the function is even, odd, or neither even nor odd.

51. $f (x) = x \sqrt{10 - x^{2}}$ $f (x) = x \sqrt{10 - x^{2}}$
52. $f (x) = \frac{x^{2} + 1}{x^{3} - 1}$ $f (x) = \frac{x^{2} + 1}{x^{3} - 1}$

Determine whether the graph is symmetric with respect to the x-axis, the y-axis, and the origin.

53. $x^{3} = y^{2} (2 - x)$ $x^{3} = y^{2} (2 - x)$
54. ${(x^{2} + y^{2})}^{2} = 2 x y$ ${(x^{2} + y^{2})}^{2} = 2 x y$
55. Show that if f is any function, then the function E defined by

$E (x) = \frac{f (x) + f (- x)}{2}$ $E (x) = \frac{f (x) + f (- x)}{2}$

is even.
56. Show that if f is any function, then the function O defined by

$O (x) = \frac{f (x) - f (- x)}{2}$ $O (x) = \frac{f (x) - f (- x)}{2}$

is odd.
57. Consider the functions E and O of Exercises 55 and 56.
1. Show that $f (x) = E (x) + O (x)$ $f (x) = E (x) + O (x)$ . This means that every function can be expressed as the sum of an even function and an odd function.
2. Let $f (x) = 4 x^{3} - 11 x^{2} + \sqrt{x} - 10$ $f (x) = 4 x^{3} - 11 x^{2} + \sqrt{x} - 10$ . Express f as a sum of an even function and an odd function.

Determine whether the statement is true or false.

58. The product of two odd functions is odd.
59. The sum of two even functions is even.
60. The product of an even function and an odd function is odd.

..................Content has been hidden....................

You can't read the all page of ebook, please click here login for view all page.

Table of Contents for 2.4 Exercise Set

Create new playlist

Sign In

Sign Up

Table of Contents for
2.4 Exercise Set