The graph of the function showing the path of a soccer ball thrown by a goalie in a video game, f(x) = –0.05x2 + 2.5x + 5.2, is used to determine the height of the ball depending on its distance from the goalie, x. how do the mathematical domain and reasonable domain compare? mathematical: 0 < x < ∞ reasonable: 0 ≤ x ≤ 25 mathematical: 0 < x < ∞ reasonable: 0 ≤ x ≤ 52 mathematical: −∞ < x < ∞ reasonable: 0 ≤ x ≤ 25 mathematical: −∞ < x < ∞ reasonable: 0 ≤ x ≤ 52

The correct option is 4.

Step-by-step explanation:

The given function is

Where f(x) is height of the ball and x is the distance.

It is a polynomial function with degree 2. All polynomial functions are defined for all real numbers, therefore the mathematical domain of the function is all real numbers.

Factorize the given function.

Put f(x)=0 to find the x intercepts.

Equate each factor equal to 0.

Therefore at x=52 and -2, the graph of f(x) intersects x-axis. Before x=-2 and after x=52 the values of f(x) is negative. Height cannot be negative, therefore reasonable domain is lie between -2 to 52.

Distance cannot be negative, therefore the reasonable domain must be positive.

Therefore the reasonable domain is and option 4 is correct.

step-by-step explanation: