Question

The function mc023-1.jpg is used to model the height of an object projected in the air, where h(t) is the height in meters and t is the time in seconds. What are the domain and range of the function h(t)? Round values to the nearest hundredth.

Answer 1

I don't have the image mc023-1.jpg. Could you either paste the formula for h(t) here or re-upload the image?

If the function is a quadratic h(t)=at^2+bt+c (with a<0, as for a projectile), here's how to get domain and range:

- Domain: physical time starts at t=0 and ends when the object hits the ground (h(t)=0). Solve at^2+bt+c=0 for the positive root t_hit. The domain is [0, t_hit]. The positive root is
t_hit = (-b + sqrt(b^2 - 4ac)) / (2a) if a<0 (use the positive root).
- Range: the maximum height occurs at the vertex t_v = -b/(2a). Compute h_max = h(t_v). The range (heights reached) is [h(0), h_max] if h(0) ≤ h_max; typically h(0)=c and the range is [0, h_max] if you consider heights until ground contact. More commonly for projectile from ground, range is [0, h_max].

Round t_hit, t_v, and h_max to the nearest hundredth.

If you give the specific h(t), I will compute the numeric domain and range and round to two decimals.