# Help with functions SVP?!

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Hey guys please help me out with this function trouble? The question and the data is in the image attached. How does one answer question a in that screenshot?

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It asks you for the roots of the function - where f(x) crosses the x-axis. The solutions are (0,0) and (4,0).

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A second question is attached, I genuinely hope you can help me, thank you!

Regarding this one , how does one find p and q? what are they symbolic of?!

Edited by DropBoite

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a) x=0, 4

b) x=2

c) I'm not too sure, but I'd say x=-2

EDIT: That was for the first Q.

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It asks you for the roots of the function - where f(x) crosses the x-axis. The solutions are (0,0) and (4,0).

Okay so If I get you that's so simple and I'm an idiot... Thanks !!

I don't know how that slipped me, could you be a darling and help me with the other question too? Thanks!

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It asks you for the roots of the function - where f(x) crosses the x-axis. The solutions are (0,0) and (4,0).

Okay so If I get you that's so simple and I'm an idiot... Thanks !!

I don't know how that slipped me, could you be a darling and help me with the other question too? Thanks!

For a) take f(x) and substitute the values x=0 and y=6 (you'll get a relation with only q and p). Then do the same for x=1 and y=4. For b) solve the system of these two equations:

p+q=6

and

0.5p+q=4

p=4 and q=2

For c) the limit as x-->+oo of 4(1/2)^x+2=2

so the horizontal asymptote is y=2

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a) x=0, 4

b) x=2

c) I'm not too sure, but I'd say x=-2

EDIT: That was for the first Q.

Thank you! Could you elaborate on how I should go about calculating the answer to question c? Thank you! Will rep that post

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It asks you for the roots of the function - where f(x) crosses the x-axis. The solutions are (0,0) and (4,0).

Okay so If I get you that's so simple and I'm an idiot... Thanks !!

I don't know how that slipped me, could you be a darling and help me with the other question too? Thanks!

For a) take f(x) and substitute the values x=0 and y=6 (you'll get a relation with only q and p). Then do the same for x=1 and y=4. For b) solve the system of these two equations:

p+q=6

and

0.5p+q=4

p=4 and q=2

For c) the limit as x-->+oo of 4(1/2)^x+2=2

so the horizontal asymptote is y=2

What are those two o's for? Okay but my math teacher didn't do this chapter well can you please tell me what p and q are? Thanks!

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Look at the graph of (1/2)^x as x tends to plus infinity. The limit of that function for high values of x is 0 so in your f(x) that part becomes zero and you only have the value of q left which is 2 so f(x) tends to y=2 as x tends to plus infinity which is why y=2 is the horizontal asymptote.

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Look at the graph of (1/2)^x as x tends to plus infinity. The limit of that function for high values of x is 0 so in your f(x) that part becomes zero and you only have the value of q left which is 2 so f(x) tends to y=2 as x tends to plus infinity which is why y=2 is the horizontal asymptote.

Apologies but you lost me, that's more jargon than I can handle!

Okay I'm looking at the guide and it says the equation of the horizontal asymp is y=c so if I have any exponential equation I can simply assume that the number c is the horizontal asymptote? Does that ALWAYS hold true? Additionally an innocent assumption tells me that when there is no c the equation of the asymp is y=0, true?

Edited by DropBoite

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Look at the graph of (1/2)^x as x tends to plus infinity. The limit of that function for high values of x is 0 so in your f(x) that part becomes zero and you only have the value of q left which is 2 so f(x) tends to y=2 as x tends to plus infinity which is why y=2 is the horizontal asymptote.

Apologies but you lost me, that's more jargon than I can handle!

Okay I'm looking at the guide and it says the equation of the horizontal asymp is y=c so if I have any exponential equation I can simply assume that the number c is the horizontal asymptote? Does that ALWAYS hold true? Additionally an innocent assumption tells me that when there is no c the equation of the asymp is y=0, true?

Hmm no you can't assume that because any exponential function a^x does not always tend to 0 for high values of x. This is the case only when 0<a<1. Anyway, the guide says that the horizontal asymptote is y=c because the horizontal asymptote is always a straight line parallel to the x-axis I think in your exercise you can see the asymptote simply by looking at the graph - especially since the command term is "write down". See how f(x) is almost parallel to the x-axis as y almost becomes 2 but never actually does?

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