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# Col Alg I ch 1

### BGSU College Algebra I, Chapter One

Question | Answer |
---|---|

1. The set of numbers {1,2,3,...} are called the ___ numbers. | natural |

2. The set of numbers {..., -3,-2,-1,0,1,2,3,...} are called the ___ . | integers |

3. The set of numbers that can be expressed as a ratio of two integers are the ___ numbers. | rational |

4. When they are in their decimal form, rational numbers will be ___ or ___ decimals. | terminating, repeating |

5. When they are in their decimal form, irrational numbers will be ___ and ___ decimals. | nonterminating, nonrepeating |

6. The set containing both rational and irrational numbers are the ___ numbers. | real |

7. A number is in scientific notation if it is in the form c x 10^n where the condition on c is that ___ and n is a/an ____. | the absolute value of c is greater than or equal to 1 and less than 10, n is an integer |

8. If you take a number whose absolute value is less than one, and rewrite it in scientific notation c x 10^n, the exponent n will be ___. | negative |

9. If you take a number whose absolute value is greater than ten, and rewrite it in scientific notation c x 10^n, the exponent n will be ___. | positive |

10. If you have a number in exponential notation, k x 10^m, where |k|<1, and rewrite it in scientific notation, c x 10^n, the new exponent n will be ___ than the old exponent m. | smaller |

11. If you have a number in exponential notation, k x 10^m, where |k|>10, and rewrite it in scientific notation, c x 10^n, the new exponent n will be ___ than the old exponent m. | bigger |

12. The name we use for a set of ordered pairs is a ___. | relation |

13. We often use the notation (x,y) to name a set of ordered pairs. The set containing all of the x's is called the ___. | domain |

14. We often use the notation (x,y) to name a set of ordered pairs. The set containing all of the y's is called the ___. | range |

15. A relation between two sets so that each member of the first set goes with exactly one member of the second set is called a ___. | function |

16. A function is a ___ between ___ ____ so that each member of the ___ corresponds to ___ ___ member of the ___. | relation, two sets, domain, exactly one, range |

17. We can determine whether a graph is that of a function by applying the Vertical Line Test. The graph is that of a function if ___. | every vertical line crosses the graph at most once |

18. The easiest way to show that a relation is not a function is to find one member of the ___ that goes with two members of the ___. | domain, range |

19. For a function f, f(a)=b means the point __ is a point on the graph. | (a,b) |

20. For a function f, if the point (a,b) is a point on the graph, then f(__)=___. | a,b |

21. If f(a)=b, then the function sends the x-value ___ to the y-value ___. | a, b |

22. We read the symbols "f(x)" as___. | f of x |

23. If you are given the graph of f, and are asked to find f(a) for some number a, you find the point on the graph where the ___-value is a, then find the ___-value of that point. The answer to f(a) is that ___-value. | x,y,y |

24. If you are given the graph of f, and are asked to solve f(x)=b for some number b, you find the point(s) on the graph where the ___-value is b, then find the ___-value of that/those point(s). The answer to f(x)=b is that/those ___-value(s). | y,x,x |

25. For a function f, the formula to find the average rate of change of f from a to b is ___. | (f(b)-f(a))/(b-a) |

26. For a function f, the formula to find the average rate of change of f as x increases from x1 to x2 is ___. | (f(x2)-f(x1))/(x2-x1) |

27. Suppose that the graph of f contains the points (x1, y1) and (x2, y2). Then, the average rate of change of f as x increases from x1 to x2 is ___. | (y2 - y1)/(x2 - x1) |

28. The slope of the line containing the points (x1, y1) and (x2, y2) is ___. | (y2 - y1)/(x2 - x1) |

29. If f is a linear function, then the slope of the function between x1 and x2 is ___. | (f(x2)-f(x1))/(x2-x1) |

30. If a function can be written in the form f(x)=ax+b, where a and b are numbers, it is called a ___ function. | linear |

31. For a linear function f(x)=ax+b, a is the ___ and b is the __. | slope, y-intercept |

32. The point where a graph crosses the y-axis is called the ___ of the graph. | y-intercept |

33. We say a graph is increasing on the interval a < x < b if, as you move along the graph from left to right, between x=a and x=b, the y-values get ___. | bigger |

34. We say a graph is decreasing on the interval a < x < b if, as you move along the graph from left to right, between x=a and x=b, the y-values get ___. | smaller |

35. What is the interval notation for the set of x's that are greater than a and less than b? | (a,b) |

36. What is the interval notation for the set of x's that are greater than or equal to a and less than or equal to b? | [a,b] |

37. What is the interval notation for the set of x's that are greater than or equal to a and less than b? | [a,b) |

38. What is the interval notation for the set of x's that are greater than a and less than or equal to b? | (a,b] |