Answer:
The correct option is 4.
Step-by-step explanation:
The given function is
[tex]f(x)=-0.05x^2+2.5x+5.2[/tex]
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.
[tex]-\infty<x<\infty[/tex]
Factorize the given function.
[tex]f(x)=-0.05(x^2-50x-104)[/tex]
[tex]f(x)=-0.05(x^2-50x-104)[/tex]
[tex]f(x)=-0.05(x^2-52x+2x-104)[/tex]
[tex]f(x)=-0.05(x(x-52)+2(x-52))[/tex]
[tex]f(x) = -0.05 (x - 52) (x + 2)[/tex]
Put f(x)=0 to find the x intercepts.
[tex]0 = -0.05 (x - 52) (x + 2)[/tex]
Equate each factor equal to 0.
[tex]x=52,-2[/tex]
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.
[tex]0\leq x\leq 52[/tex]
Therefore the reasonable domain is [tex]0\leq x\leq 52[/tex] and option 4 is correct.
