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    For part b) there is an asymptote at y=0 so how can the graph have two roots?? Could someone explain the understanding to me please. Name:  Screenshot_20160526-142722.png
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    You've misunderstood the question. It is asking for the set of values of y (values that k can take) for there to be 2 roots.

    A root here will be where y=k and y=f(x) intersect.
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    From what i see, its specifically saying the function f(x) = k has two roots, and its not referring to the graph of y = f(x).
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    (Original post by Parallex)
    You've misunderstood the question. It is asking for the set of values of y (values that k can take) for there to be 2 roots.

    A root here will be where y=k and y=f(x) intersect.
    (Original post by MAS98)
    From what i see, its specifically saying the function f(x) = k has two roots, and its not referring to the graph of y = f(x).
    I don't think I get it. How would I find k in this case?

    I've come across the same question from another paper and I'm stumped again.
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    (Original post by Ravster)
    I don't think I get it. How would I find k in this case?

    I've come across the same question from another paper and I'm stumped again.
    You're right y=0 is an asymptote so for f(X)=k we know that k must be a negative so when we subtract k to both sides f(X) +k it shifts the curve upwards. The range where the curve will intersect the X axis twice (two solutions) will be between 0 since it's an asymtpote and at your minimum point from (a) since translating the curve upwards by more than your minimum point will leave you with 0 solutions.
 
 
 
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