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Determine the intervals on which the function is continuous

  1. Jan 27, 2014 #1
    1. The problem statement, all variables and given/known data

    Determine the intervals on which the function is continuous, support with graph.
    15) f(x)=x^2+(5/x)

    16) g(g)= 5-x, x<1
    2x-3, x>1

    17) f(x)=√(4/(x-8))


    2. Relevant equations



    3. The attempt at a solution
    I understand the concept behind not being able to have 0/0. Therefore any breaks where x causes the denominator to equal zero would be a discontinuity in the graph.
    Most of the problems I have done have had a polynomial where I could factor and then clearly see any denominator values that cause a zero.

    15) for this problem I made x^2+(5/x) into (x^3 +5)/ x from here i am not sure where to go since the only thing i can see is that here x cannot equal zero or the denominator will cause a 0/0 effect
    when I graph it as well I get an unusual graph as well

    16) The only thing I can see to do would be plug in 1 for x resulting in 5-1 = 4 and 2*1-3=-1

    17) Here I got rid of the square root by multiplying the function by itself to get 4/(x-8) With this i can visually see that x cannot equal 8. So possibly the intervals would be [8, infinity)

    If anyone could help guide me in the right direction on how to approach the problems as well as confirm or deny 17 as being correct it would be greatly appreciated.
     

    Attached Files:

  2. jcsd
  3. Jan 27, 2014 #2

    haruspex

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    Exactly
    Right again. So your answer is?
    [8, infinity) includes 8 - you need to exclude it. There's also < 8.
     
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