Results 1 to 5 of 5

Math Help - Algebra: Solving Inequalities - TWO PROBLEMS

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    3

    Algebra: Solving Inequalities - TWO PROBLEMS

    Problem #1: If you have pieces of paper in one box with the numbers 0, 1, 2, 3, 4 on them and pieces of paper in a second box with the numbers 5, 6, 7, 8, 9 on them, explain how you could form five ordered pairs that would represent a function and five ordered pairs that would represent a relation. Explain your reasoning.

    1. Explain how you could form five ordered pairs that would represent a function and five ordered pairs that would represent a relation.


    2. Explain your reasoning.


    ----- ----------- -------- ------------- --------------- --------


    Problem #2 : Which of the following ski runs would present the greatest challenge? Why? Run #1, which has a vertical change of 100 feet for each horizontal change of 500 feet, or Run #2 which has a vertical change of 100 feet and a horizontal change of 1000 feet.


    Find the slope of each run to justify your answer. It may be helpful to draw a picture of both runs as close to scale as possible. Explain your reasoning.


    1. Which of the ski runs would present the greatest challenge?


    2. Explain your reasoning.




    I appreciate all help, thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor undefined's Avatar
    Joined
    Mar 2010
    From
    Chicago
    Posts
    2,340
    Awards
    1
    Quote Originally Posted by a360236 View Post
    Problem #1: If you have pieces of paper in one box with the numbers 0, 1, 2, 3, 4 on them and pieces of paper in a second box with the numbers 5, 6, 7, 8, 9 on them, explain how you could form five ordered pairs that would represent a function and five ordered pairs that would represent a relation. Explain your reasoning.

    1. Explain how you could form five ordered pairs that would represent a function and five ordered pairs that would represent a relation.


    2. Explain your reasoning.


    ----- ----------- -------- ------------- --------------- --------


    Problem #2 : Which of the following ski runs would present the greatest challenge? Why? Run #1, which has a vertical change of 100 feet for each horizontal change of 500 feet, or Run #2 which has a vertical change of 100 feet and a horizontal change of 1000 feet.


    Find the slope of each run to justify your answer. It may be helpful to draw a picture of both runs as close to scale as possible. Explain your reasoning.


    1. Which of the ski runs would present the greatest challenge?


    2. Explain your reasoning.




    I appreciate all help, thanks!
    Problem 1 is about relation versus function. See this link.

    Question two is about slope. Steeper means more difficult. In the case of positive slope, greater slope means steeper.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2010
    Posts
    3
    I still do not understand, but thanks!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor undefined's Avatar
    Joined
    Mar 2010
    From
    Chicago
    Posts
    2,340
    Awards
    1
    Quote Originally Posted by a360236 View Post
    I still do not understand, but thanks!
    Well, it helps to have concrete examples and an "intuitive feel" for the concepts rather than just relying on formal definitions.

    To tell the truth, you might not have a good feel for the (real) formal definitions for some time, because they are usually introduced at University level. But the concepts themselves are not hard.

    Possibly the relation that's most familiar to you is the "is equal to" relation. Suppose we're only dealing with the numbers {0, 1, 2, 3, ...}. Then, for our purposes, the "is equal to" relation is precisely given by the set {(0,0), (1,1), (2,2), (3,3), ...}.

    When we say 5 = 5, that means that (5,5) is in the relation "is equal to". When we say 5 \neq 6, that means (5,6) is not in the relation "is equal to".

    Another way to say this is that "5 is related to 5 by the 'is equal to' relation."

    So for a pair of sets like A = {1, 2, 3, 4} and B = {a, b, c, d}, we can make up relations simply by listing ordered pairs (any pairs we choose), in which the first element is from the first set, and the second element is from the second set.

    An example is C = {(1, b), (1, c), (2, a), (3,d), (4, d)}.

    (This whole definition is a little watered down. Here the relation is defined as C, but the "real" definition of relation would be the ordered triple (A, B, C). I doubt your teacher would expect you to know this.)

    An example of a function that you might have experience with is the square root function. What's special about functions is that given some input, there is a unique value associated with it by the function.

    Suppose we're just working with the numbers {0, 1, 2, 3, ...}. Then the square root function will only be defined for the input values {0, 1, 4, 9, 16, ...}, which is the domain, and the function can be described by the set {(0,0), (1,1), (4,2), (9,3), (16,4), ...}.

    Note that the set C above is not a function because the value 1 is associated with 2 values, b and c. For it to be a function, each value in A must be associated with exactly 1 value in B.

    Slope is a whole other concept, and since this post is getting long, I'll just leave it at that for now. If you'd like me to explain slope, I can, but maybe you don't like or understand my explanation for relations and functions, so one thing at a time.
    Last edited by undefined; May 6th 2010 at 11:43 AM. Reason: minor adjustments
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    May 2010
    Posts
    3
    Thanks for all the help! I think I have got it now! Thanks again!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Problems solving some inequalities questions
    Posted in the Algebra Forum
    Replies: 9
    Last Post: March 29th 2011, 02:39 PM
  2. Algebra: Inequalities
    Posted in the Algebra Forum
    Replies: 7
    Last Post: July 9th 2010, 01:14 AM
  3. Replies: 1
    Last Post: January 28th 2010, 11:21 AM
  4. Replies: 45
    Last Post: August 5th 2009, 10:31 PM
  5. Solving Problems Involving Inequalities
    Posted in the Algebra Forum
    Replies: 1
    Last Post: September 22nd 2008, 08:19 PM

Search Tags


/mathhelpforum @mathhelpforum