Successfully reported this slideshow.
We use your LinkedIn profile and activity data to personalize ads and to show you more relevant ads. You can change your ad preferences anytime.
Solving Rational Inequalities

 Where is this true?


 Notice, we're asking when is       positive?


 Or, graphically, fo...
As we can see, f(x) changes sign when x = 0, and 
rather dramatically when x = 1.

Notice it's crossing the x­axis when th...
This observation suggests a method of solving analytically.




 numerator: x = 0                 denominator: x ­ 1 = 0
 ...
Example 2:         For our method to work, it is 
                   essential that one side is 0!



                 Com...
Now to find where the numerator 
               and denominator = 0!

 Numerator:                 Denominator:




       ...
Let's check this by graphing 
                                Recall, we said this 
                                functi...
Practice:
                                         (notice it wants solutions 
                                         wh...
numerator = 0                   denominator = 0
when x = 1                      when x = ­2




                ­2        ...
numerator = 0       denominator = 0
   nowhere!            x = 1




                1
     negative         positive
    ...
numerator = 0                    denominator = 0
       x = ­2, x = ­3                   x = ­1, x = 5


           ­3    ...
Upcoming SlideShare
Loading in …5
×

Day 8 - Rational Inequalities

997 views

Published on

Solving Rational Inequalities

Published in: Education
  • Be the first to comment

Day 8 - Rational Inequalities

  1. 1. Solving Rational Inequalities Where is this true? Notice, we're asking when is  positive? Or, graphically, for what x is  above the x­axis?  To know this, we need to know where f(x) changes sign. Graph f(x) in Y1 in your calculator, and see if you can tell  where f(x) changes sign. Where does it go from being below  the x­axis, to above it? Or vice versa?
  2. 2. As we can see, f(x) changes sign when x = 0, and  rather dramatically when x = 1. Notice it's crossing the x­axis when the numerator is zero,  and the vertical asymptote occurs when the denominator is  zero. Expected solution of     is...
  3. 3. This observation suggests a method of solving analytically. numerator: x = 0 denominator: x ­ 1 = 0    x = 1 true false true 0 1 Check ­10: Check .5: Check 10: What values of x make the inequality true? or we could write: 
  4. 4. Example 2: For our method to work, it is  essential that one side is 0! Combine terms so we can  consider one fraction! continued...
  5. 5. Now to find where the numerator  and denominator = 0! Numerator: Denominator: ­3 ­2 2 Solution:
  6. 6. Let's check this by graphing  Recall, we said this  function is above the  x­axis when 
  7. 7. Practice: (notice it wants solutions  when ≤ 0. Where is it  A) NEGATIVE?) B) C) (solutions provided on following slides...)
  8. 8. numerator = 0 denominator = 0 when x = 1 when x = ­2 ­2 1 positive negative positive    F T F solution: 
  9. 9. numerator = 0 denominator = 0 nowhere! x = 1 1 negative positive F T solution: x > 1
  10. 10. numerator = 0 denominator = 0 x = ­2, x = ­3 x = ­1, x = 5 ­3 ­2 ­1 5 positive negative negative positive positive F T T F F Solution: 

×