Final answer:
The equation h(x) = −11x + 330 models the elevation of a hot air balloon, descending over time. The domain is practically from 0 to 30 seconds, and the range is from 0 to 330 feet, representing the elevation from the ground to its initial height.
Step-by-step explanation:
The equation h(x) = −11x + 330 models the elevation of a hot air balloon in feet with respect to time x in seconds since the balloon was first noticed. To graph this function, we plot h(x) against x on a coordinate plane, with x as the horizontal axis and h(x) as the vertical axis. The graph is a straight line with a negative slope because the coefficient of x is negative. We start the line at h(0) = 330, indicating the balloon's elevation when first noticed, and extend this line downward to the right to indicate the decreasing elevation over time.
The domain of the function, in a real-life context, is defined by the time over which we observe the balloon, usually from the moment we start observing (x = 0) until the balloon lands (h(x) = 0). Mathematically, the domain could extend indefinitely, but realistically it is limited to nonnegative values of x up to the point where the balloon reaches the ground. To find the time when the balloon lands, we set h(x) = 0 and solve for x, resulting in x = 330 / 11 = 30 seconds. Thus, the practical domain is [0, 30].
The range represents possible values of h(x), the elevation of the balloon. Initially, the balloon is at 330 feet, and it cannot have a negative elevation, so the range is [0, 330].