Graphs and asymptotes, c3/c4

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.

Reply 1

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.

Reply 2

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).

Reply 3

Ravster

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.

Reply 4

Middriver

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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Graphs and asymptotes, c3/c4

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