Results 1 to 12 of 12
Like Tree2Thanks
  • 1 Post By skeeter
  • 1 Post By Plato

Math Help - Question About Test Points

  1. #1
    Junior Member
    Joined
    Mar 2012
    From
    LA
    Posts
    68

    Question About Test Points

    This is for Nonlinear inequalities in one variable, via solving the quadratic inequalities. I also have to put the solution set in interval notation.

    For example.

    X-5/X-7>(or equal to) 0.

    First I have to find the denominator that makes the value to 0. So this will be X=7. But also the numerator gets changed to x=5. What my question is, is the test point really needed? Because can't you just look at the solution and see if the number is greater than(or equal to)0?. 5>0 or 7>0. Neither of these are true so the notation set would look like (5,7), right? But also, about the test points, the numbers that get plugged into the variables, are they just random numbers I can pick and choose from?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1

    Re: Question About Test Points

    Quote Originally Posted by Past45 View Post
    This is for Nonlinear inequalities in one variable, via solving the quadratic inequalities. I also have to put the solution set in interval notation.

    For example. X-5/X-7>(or equal to) 0.
    Please use grouping symbols.
    Is it x-\frac{5}{x-7}\ge 0~? OR is it \frac{x-5}{x-7}\ge 0~?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Mar 2012
    From
    LA
    Posts
    68

    Re: Question About Test Points

    it's the second one.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1

    Re: Question About Test Points

    Quote Originally Posted by Past45 View Post
    it's the second one.
    On what intervals do both numerator and denominator have same sign?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Mar 2012
    From
    LA
    Posts
    68

    Re: Question About Test Points

    Not too sure, I am looking through my book and I do not have a similar problem like that(nor do my notes show a problem with the numerator and denominator with the same symbols), I am going to assume I wrote it wrong the denominator is suppose to be x+5.

    So that would make the interval notation be (-∞,-7]U[5,∞)

    Quote Originally Posted by Plato View Post
    On what intervals do both numerator and denominator have same sign?
    Last edited by Past45; April 3rd 2012 at 01:51 PM.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426

    Re: Question About Test Points

    \frac{x-5}{x-7} \ge 0

    critical values are x = 5 and x = 7

    test a single value in the each of the following intervals ...

    (-\infty,5]

    [5,7)

    (7,\infty)

    since the function is continuous in each interval, if one value in the interval makes the inequality true, then all values in that interval will likewise.
    Thanks from Past45
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1

    Re: Question About Test Points

    Quote Originally Posted by Plato View Post
    On what intervals do both numerator and denominator have same sign?
    The answer is (-\infty,5]\cup(7,\infty). WHY?
    Why is 5 included and 7 not included?
    Thanks from Past45
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    Mar 2012
    From
    LA
    Posts
    68

    Re: Question About Test Points

    Because the 5 goes through the 7 when the answer has the ∞. I thought the answer would been [5,∞) tbh, since both 5 and 7 are greater than 0. I did not think they would have a union.

    But is a test really needed to get the answer?

    Quote Originally Posted by Plato View Post
    The answer is (-\infty,5]\cup(7,\infty). WHY?
    Why is 5 included and 7 not included?
    Follow Math Help Forum on Facebook and Google+

  9. #9
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1

    Re: Question About Test Points

    Quote Originally Posted by Plato View Post
    The answer is (-\infty,5]\cup(7,\infty). WHY?
    Why is 5 included and 7 not included?
    See reply #5.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Junior Member
    Joined
    Mar 2012
    From
    LA
    Posts
    68

    Re: Question About Test Points

    That is true, for this problem it is. I did 3 test points, -3, which the answer came out to be 2 over 5 is greater or equal to 0. Then I did 0, and 5 over 7 is greater than or equal to 0. Then I did 1 and the answer was 2 over 3 is greater or equal to 0.

    I have to apologize(seems like I am repeating the question), only thing that is why there is a union when 5 is greater than 0, and we start with (-∞ to 5) U... I would of thought the answer would of been [5,∞).

    Quote Originally Posted by skeeter View Post
    \frac{x-5}{x-7} \ge 0

    critical values are x = 5 and x = 7

    test a single value in the each of the following intervals ...

    (-\infty,5]

    [5,7)

    (7,\infty)

    since the function is continuous in each interval, if one value in the interval makes the inequality true, then all values in that interval will likewise.
    Follow Math Help Forum on Facebook and Google+

  11. #11
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,621
    Thanks
    426

    Re: Question About Test Points

    Quote Originally Posted by Past45 View Post
    That is true, for this problem it is. I did 3 test points, -3, which the answer came out to be 2 over 5 is greater or equal to 0. Then I did 0, and 5 over 7 is greater than or equal to 0. Then I did 1 and the answer was 2 over 3 is greater or equal to 0.

    I have to apologize(seems like I am repeating the question), only thing that is why there is a union when 5 is greater than 0, and we start with (-∞ to 5) U... I would of thought the answer would of been [5,∞).
    -3, 0 , and 1 are in the same interval, (-\infty, 5) ... how about choosing one value in each of the three distinct intervals?

    (-\infty, 5) ... x = -3

    (5,7) ... x = 6

    (7, \infty) ... x = 8

    you know the inequality is true at x = 5, because it makes the inequality equal 0. A vertical asymptote exists at x = 7 ... the value of the expression is negative on the left side and positive on the right side of x = 7.

    Taking a look at a graph may also help ...
    Attached Thumbnails Attached Thumbnails Question About Test Points-rational2.jpg  
    Follow Math Help Forum on Facebook and Google+

  12. #12
    Junior Member
    Joined
    Mar 2012
    From
    LA
    Posts
    68

    Re: Question About Test Points

    That was my question, how do I know which numbers to pick and choose to do a test point? For example if I pick 9, the answer will be 4 over 2 which equals 2>(or equal to) 0 which is true. It's like whatever number I pick is going to be greater than or equal to 0. If it's fraction or a whole number.

    Just one last thing, I think this one is somewhat throwing me off because both the num/dem have the same symbol. and the outcome is going to be true for all. So, I am not sure if I will come across another one like this.

    BTW, thanks for the helping hand.

    Quote Originally Posted by skeeter View Post
    -3, 0 , and 1 are in the same interval, (-\infty, 5) ... how about choosing one value in each of the three distinct intervals?

    (-\infty, 5) ... x = -3

    (5,7) ... x = 6

    (7, \infty) ... x = 8

    you know the inequality is true at x = 5, because it makes the inequality equal 0. A vertical asymptote exists at x = 7 ... the value of the expression is negative on the left side and positive on the right side of x = 7.

    Taking a look at a graph may also help ...
    Last edited by Past45; April 3rd 2012 at 10:00 PM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: August 24th 2011, 11:35 AM
  2. Replies: 1
    Last Post: February 9th 2011, 10:52 AM
  3. Replies: 5
    Last Post: November 7th 2010, 09:21 AM
  4. First derivative test, turning points
    Posted in the Algebra Forum
    Replies: 4
    Last Post: May 10th 2009, 12:11 PM
  5. Replies: 0
    Last Post: March 11th 2008, 09:28 PM

Search Tags


/mathhelpforum @mathhelpforum