Question

I need help solving this practice Having a tough time

Answer 1

The given function is:

`f(x)=-19\sin((7)/(3)x+(1)/(6))-3`

This function is written in the form:

`f(x)=A\sin(B(x+C))+D`

Where:

A is the amplitude of the function

B is given by the period=2pi/B

C is the phase shift

D is the vertical shift

By definition, the amplitude is the measure between half the wave and the crest.

To find the range of temperatures then we need to take into account the amplitude is 19, but also the function has a vertical shift of D=-3, then we need to subtract -3 to the upper and lower range, so:

The initial range given by the amplitude is: -19°F to 19°F.

When we apply the vertical shift we obtain:

-19-3=-22°F

19-3=16°F

The answer is: the range in the average rate of change in temperature of the substance is from a low temperature of -22°F to a high of 16°F.