Question

The function f(x) = 4x – 0.1x2 is used to model the curve of a bridge over a small river, where x is the distance from one side of the river and the x-axis represents the ground. The mathematical range for the function is the set of real numbers. Which statement describes the limitation for the reasonable range compared to the mathematical range? The limitation for the reasonable range restricts it to positive real numbers. The limitation for the reasonable range restricts it to positive whole numbers. The limitation for the reasonable range restricts it to real numbers greater than or equal to 0 and less than or equal to 40. The limitation for the reasonable range restricts it to whole numbers greater than or equal to 0 and less than or equal to 40.

Answer 1

Answer:

x ∈ R ( 0 , + ∞ )

Step-by-step explanation:

In the function:

F(x) = 4*x -0,1*x²

The domain of  F(x) is all the set of real numbers

R ∈ ( -∞ , +∞ )

values for F(x), can be found from negative and positive values of x

for instance for:

x = -2          F(x) = 4*(-2) - 0,1 * (-2)²        F(x) = - 8,4

x = 2           F(x) = 4*(2) - 0,1 * (2)²           F(x) = 7,6

But distance x could not be negative ( there is not negative distance in the real world), therefore the reasonable range restricts values of x only to positive values.

Then x can be any number x ≥ 0  ( distance could be 0 )