Function

[IloveManUtd]

The function g(x) = p sin x+q where p < 0 has a maximum value of 10 and a minimum value of -4. Find the values of p and q

I know that for sin graphs, p + q = maximum and -p + q = minimum, but how about this? I've tried reversing the unknowns and switching positive and negative signs but am getting no where. Please help. Thx

 

[mmm4444bot]

g(x) = p sin x + q where p < 0

I know that for sin graphs, p + q = maximum and -p + q = minimum

This is only true, if p > 0.

Since, in your exercise, p < 0, switch your formulas for maximum and minimum.

p + q = -4

q - p = 10

Solving this system for p and q is easy.

Another way is to first find the function's amplitude because that's |p|.

In a sinusoidal curve, the distance from the peak to the valley (range) is twice the amplitude, yes?

2 * |p| = maximum - minimum

Solve this equation for p. That will give you the range when q = 0 .

Then, think how many units (q) you need to shift the curve up, so that valley-to-peak goes from -4 to 10, instead of from p to -p.

I welcome specific questions.