Please solve this nasty question

[chio]

I cant solve this problem.
When I think I found the answer and put the xy values in the eqation, I realize it is wrong answer.

 

[mmm4444bot]

Please show your attempt. Mistakes may be fixable. Thank you.

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[Otis]

Hi chio. I'm thinking that four different functions produce such a graph. Did you start with the general transformed cosecant function?

f(x) = a csc(bx + c) + d

If not, then please also share what class you're taking, as well as what has been discussed recently.

?

 

[Otis]

Hint: d = 1 by inspection because y=1 is midway between the minimums (-4) and the maximums (6).

 

[Otis]

Another Hint: In cosecant and secant curves, the parameter 'a' controls vertical distance between minimums and maximums. The animation below shows how that distance increases as |a| changes from 1 to 9.

 

[Otis]

Thus far, we know that |a|=5 and d=1. Therefore, one possible equation is:

y = 5 csc(bx + c) + 1

We're given values for two (x,y) pairs satisfying the equation above. Substituting each yields a system of two equations that solves nicely for b and c.

Hint: First, solve each equation for csc(bx+c), and then consider x-values near zero where csc(x) equals ±1.

 

[Steven G]

I would first find the equation of the corresponding sine function, y=Asin(Bx+C)+D.
Recall that a period of sine (and cosine) graph starts when the angle equals 0 and ends when the angle equals 2pi.

The sine graph goes from -4 to 6. (6)-(-4) = 10. The amplitude is A= 10/2 = 5. The graph is therefore raised 1 unit, so D = 1.
It just remains to find B and C.

Think about how to solve for B and C!