Respuesta :
Solution:
In the given function b(t), the variable t represents the number of years after 2008. The domain of this function is [tex][0,\infty )[/tex]. The range more than 258.7 would not make sense. The graph of the function is always continuous.
Explanation:
The given function b(t) shows the population of bobcats in northern Arizona since 2008. Therefore the variable t represents the number of years after 2008.
Since t represents the number of years after 2008, which is either positive or zero, therefore the domain of this function is [tex][0,\infty )[/tex].
The given function is a quadratic function and the coefficient of [tex]t^2[/tex] is negative, so it is a downward parabola. The range above the y-coordinate of the vertex doesn't make any sense.
The vertex of parabola is defined by [tex]v(-\frac{b}{2a},f(-\frac{b}{2a}))[/tex].
Vertex of the given function is (4.2,258.7).
Thus, the range more than 258.7 would not make sense for this function.
Since the given function is a polynomial function and polynomial functions are always continuous, therefore the graph of the function is always continuous.
Domain of a function is the set of all the possible input values which are valid for that function.
- A) In the given problem the variable [tex]t[/tex] represent the time.
- B) The domain of the function is zero to infinity [0, ∞]
- C) The range values which would not make sense for this function is more than 258.7.
- D) The graph be continuous.
What is domain and range of function?
Domain of a function is the set of all the possible input values which are valid for that function.
Range of a function is the set of all the possible output values which are valid for that function.
Given information-
The population of bobcats in northern Arizona since 2008 can be modeled using the function,
[tex]b(t) = -0.32t^2 + 2.7t + 253.[/tex]
- A) Variable t represent-As the modeled function given in the problem represents the population of Arizona since 2008. Thus in the given problem the variable [tex]t[/tex] represent the time.
- B)The domain for this function-As the modeled function given in the problem represents the population and the population can only be a positive and real number or zero. Thus the domain of the function is zero to infinity [0, ∞]
- C)The range values which would not make sense for this function-
The given function is,
[tex]b(t) = -0.32t^2 + 2.7t + 253.[/tex]
The above equation if the equation of parabola. The vertex of the parabola can be given as,
[tex]v=(\dfrac{-b}{2a}, f(\dfrac{-b}{2a}))[/tex]
As the value of [tex]b[/tex] is 2.7 and value of a is [tex]-0.32[/tex]. Thus,
[tex]v=(4.2,258.7)[/tex]
Hence, the range values which would not make sense for this function is more than 258.7.
- D)The graph be continuous or discrete-The given modeled function is a polynomial equation of degree 2. As the polynomial function are always continues. Thus the graph be continuous.
Hence,
- A) In the given problem the variable [tex]t[/tex] represent the time.
- B) The domain of the function is zero to infinity [0, ∞]
- C) The range values which would not make sense for this function is more than 258.7.
- D) The graph be continuous.
Learn more about the domain and range of the function here;
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