How do mathematical domains and reasonable domain compare

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weekly income y:
y = 10x
where x is number of hours worked per week
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domain: x >= 0 hours
range: y >= 0 dollars
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Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
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b all real numbers x>4

Step-by-step explanation:

edg 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.

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