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a helicopter that is 2000 meters above the ground at a rate of 2 meters per second. The altitude of the helicopter after t seconds is given h(t0+2000-2t.

Give the range of this function and give the domain of this function. 
Algebra 1 

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Can you double check this question. Should it be H=2000-2t? Is the helicopter descending at this rate?
 
The range is all possible y values and domain is all possible x values. It might be helpful to graph this equation.

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1 Answer

h(t) = 2000 - 2t    (You need to be careful to write the equation down correctly.)
 
The domain is all values of t that are valid inputs to h(t).  The range is the values that h(t) can take on.
 
Looking at h(t), the -2t term makes h(t) smaller as t increases, so the largest value of h(t) is 2000, when t=0. When t = 1000, then h(t) = 0; that is, the helicopter has landed on the ground.  If we assume the helicopter doesn't burrow underground, then h(t) has a minimum value of zero.  So the range of h(t) is 0 ≤ h(t) ≤ 2000, or [0,2000] in interval notation.
 
The domain is 0 ≤ t ≤ 1000, or [0,1000] in interval notation.  We do not know what the helicopter was doing in the past (it may have been climbing, descending, turning, or flying straight and level), so the function may not be valid for values of t < 0.  For values of t > 1000, h(t) becomes negative, which means it continues to descend after landing, which is also not valid.  So t is limited to the values between 0 and 1000 seconds.