1. Concepts and Vocabulary
Chapter 2 Review
Concepts and Vocabulary

2. Q1.
If a function is defined by the equation y = f(x), then x is called the _?_ variable and y is the _?_ variable.

3. A1.
independent
dependent

4. Q2.
A set of points in the xy-plane is the graph of a function if and only if every _?_ line intersects the graph in at most one point.

5. A2.
vertical

6. Q3.
The set of all images of the elements in the domain of a function is called the _?_.

7. A3.
range

8. Q4.
True or False:
Every relation is a function.

9. A4.
False

10. Q5.
True or False:
The y-intercept of the graph of the function y = f(x), whose domain is all real numbers, is f(0).

11. A5.
True

12. Q6.
True or False:
The independent variable is sometimes referred to as the argument of the function.

13. A6.
True

14. Q7.
For the graph of the linear function f(x) = mx + b, m is the _?_ and b is the _?_.

15. A7.
slope
y-intercept

16. Q8.
True or False:
The correlation coefficient is a measure of the strength of a linear relation between two variables and must lie between -1 and 1, inclusive.

17. A8.
True

18. Q9.
The average rate of change of a function equals the _?_ of the secant line.

19. A9.
slope

20. Q10.
A function f is _?_ on an open interval if for any choice of x1 and x2 in the interval, with x1<x2, we have f(x1) < f(x2).

21. A10.
increasing

22. Q11.
An _?_ function f is one for which f(-x) = f(x) for every x in the domain of f.

23. A11.
even

24. Q12.
An _?_ function f is one for which f(-x) = -f(x) for every x in the domain of f.

25. A12.
odd

26. Q13.
True or False:
Even functions have graphs that are symmetric with respect to the origin.

27. A13.
false

28. Q14.
The graph of f(x) = mx + b is decreasing if m is _?_ than zero.

29. A14.
less

30. Q15.
When functions are defined by more than one equation, they are called _?_ functions.

31. A15.
piecewise

32. The cube function is odd and is increasing on the interval (- ∞, ∞).
Q16.
True or False:
The cube function is odd and is increasing on the interval (- ∞, ∞).

33. A16.
true

34. Q17.
True or False:
The domain and range of the reciprocal function are the set of all real numbers.

35. A17.
false

36. Q18.
Given f(x), then the graph of y = f(x – 2) may be obtained by a(n) _?_ shift of the graph of f a distance of 2 units to the _?_.

37. A18.
horizontal
right

38. Q19.
Given f(x), then the graph of y = f(-x) may be obtained by a reflection about the _?_-axis of the graph of the function y = f(x).

39. A19. y

40. Q20.
Given f(x), then the graph of y = 3f(x) may be obtained by a vertical _?_ of the graph of f by a factor of _?_.

41. A20.
stretch 3

42. Q21.
True or False:
The graph of y = - f(x) is the reflection about the x-axis of the graph of y = f(x).

43. A21.
true

44. Q22.
True or False:
To obtain the graph of y = f(x+2) – 3, shift the graph of y = f(x) horizontally to the right 2 units and vertically down 3 units.

45. A22.
false

46. Q23.
True or False:
To obtain the graph of y = f(4x), horizontally compress the graph of y = f(x) by a factor of 4 . That is, divide each x-coordinate on the graph of y = f(x) by 4.

47. A23.
true

48. Q24.
If the domain of f is all real numbers in the interval [0,7], and the domain of g is all real numbers in the interval [-2,5], then the domain of f + g is all real numbers in the interval _?_.

49. A24.
[0,5]

50. Q25.
The domain of f/g consists of all real numbers x for which g(x) _?_ 0 that are in the domains of both _?_ and _?_.

51. A25. ≠ f g

52. If f(x) = x + 1 and g(x) = x³, then _?_ = (x + 1)³ .
Q26.
If f(x) = x + 1 and g(x) = x³, then _?_ = (x + 1)³ .

53. A26.
g(f(x))

54. Q27.
True or False:
f(g(x)) = f(x)· g(x)

55. A27.
false

56. Q28.
True or False:
The domain of (f· g)(x) consists of the numbers x that are in the domains of both f and g.

57. A28.
true

58. Q29.
True or False:
The domain of the composite function (f ◦ g)(x) is the same as the domain of g(x).

59. A29.
false

60. What is the best way to study for a Math test?
Q30.
What is the best way to study for a Math test?

61. A30.
Work problems!