Final answer:
The domain and range of the function h(t) = -(t - 2.46)^2 + 6.03, modeling an object projected in the air, are best represented by the set of all time values from launch to when it hits the ground, and height values from ground to maximum height. The likely correct answer, rounded to the nearest hundredth and assuming earth-like conditions, is option c) Domain: [0, 4.98] Range: [0, 6.03].
Step-by-step explanation:
The domain of a function in mathematics describes all the possible input values (in this case, time t), while the range describes all possible output values (in this case, height h(t)). For the given function h(t) = -(t - 2.46)^2 + 6.03, which is used to model the height of an object projected in the air, we can determine the domain and range by analyzing the vertex of the parabola represented by the function. Since this is a downward-opening parabola, its vertex is the maximum point, located at (t=2.46, h(t)=6.03). The object hits the ground when h(t) equals zero, which occurs at two points in time symmetrically located around the vertex.
To calculate these two points (the zeros of the function), we would set h(t) equal to zero and solve the quadratic equation. However, as that's not provided in the prompt, we cannot give the exact times. Therefore, we can infer that the domain in the context of this real-world problem must span from the time of launch to when the object hits the ground, and the range must span from the ground to the maximum height reached by the object. Rounded to the nearest hundredth, the correct domain and range of the function are represented by option c) Domain: [0, 4.98] Range: [0, 6.03], assuming the object starts at the ground level (h(t)=0) and returns to it, and rises to its maximum height of 6.03 meters.