Expert: Paul Klarreich - 4/3/2008

Question
Figure 9.1

h(x) = x-9 over |x-9|

Given Figure 9.1, tell where h is continous. (Give your answer in interval form.)

Answer
Questioner:   Andrea
Category:  Calculus
Private:  No
 
Subject:  Calculus 1
Question:  Figure 9.1

h(x) = x-9 over |x-9|

Given Figure 9.1, tell where h is continous. (Give your answer in interval form.)
....................................................
Hi, Andrea,

The definition of absolute value is:


| something | = { the something, when  the something >= 0
               { the opposite of the something, when  the something < 0

So

| (x - 9) | = {   (x - 9), when  (x - 9) >= 0
             { - (x - 9), when  (x - 9) < 0

which means
 
| (x - 9) | = {   (x - 9), when  x - 9 >= 9
             { - (x - 9), when  x  < 9

and thus:
        x - 9
h(x) = ---------, which means:
      | x - 9 |


          x - 9
h(x) = { ---------, when  x >= 9
          x - 9  
          x - 9
      { ---------, when  x < 9
        -(x - 9)

which means:

 
         
h(x) = {  1, when  x >= 9
      { -1, when  x < 9

So I think h(x) is not continuous at  x = 9


Note: It is not right of you to ask more than one question at a time.  It uses up my quota and may prevent someone else from asking a question.  You can put two questions into a single submission.

I will hold your next question until I see you have read this answer.

But next time, indicate what you tried to do already. PLEASE read my instructions to questioners.

And what was figure 9.1?