The function 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.
no way to tell, but I'd say the domain is all real numbers where f(t) >= 0
The range would be 0 <= y <= vertex of parabola
The domain of the function h(t) represents the possible values for the independent variable, t (time in seconds). In this case, the height of an object can be measured for any positive value of time, starting from 0 seconds and continuing indefinitely. Therefore, the domain of the function h(t) is all real numbers greater than or equal to 0.
The range of the function h(t) represents the possible values for the dependent variable, h (height in meters). Since the height of an object can be any positive value, the range of the function h(t) is all real numbers greater than 0.
To determine the domain and range of the function h(t), we need to consider the possible values for the independent variable (t) and the dependent variable (h(t)).
Domain:
The domain of a function is the set of all possible input values for the independent variable. In this case, since t represents time, we need to consider the realistic range of time values. Generally, time cannot be negative, so the domain starts at t = 0. However, it can continue indefinitely, so the domain is t ≥ 0.
Range:
The range of a function is the set of all possible output values for the dependent variable. In this case, h(t) represents the height of the object. The height can be any positive value, including zero, when the object is on the ground. However, it can't be negative since negative height doesn't make sense in this context. Therefore, the range is h(t) ≥ 0.
So, the domain is t ≥ 0 and the range is h(t) ≥ 0.