The graph of the function f(x) = (x +2)(x + 6) is shown below. What is true about the domain and range of the function? The doma
2 answers:
Answer: The domain is all real numbers, and the range is all real numbers greater than or equal to –4.
Step-by-step explanation:
Since, the given function is,
f(x) = (x+2)(x+6)
⇒
Which is the equation of parabola, ( that opened up)
Since, the vertex of the parabola is (-4,-4)
Therefore, the value of y will be not less than -4 ( because it is an upward parabola)
Thus, the range of the given function is all real number greater than or equal to –4.
Also, we know that the domain of all parabola is always the set of real numbers.
Thus, the domain of the given function is the set of all real numbers.
Therefore, first option is correct.
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Answer:
Approximately (
.) (Assume that the choices of the
passengers are independent. Also assume that the probability that a passenger chooses a particular floor is the same for all
floors.)
Step-by-step explanation:
If there is no requirement that no two passengers exit at the same floor, each of these passenger could choose from any one of the
floors. There would be a total of
unique ways for these
passengers to exit the elevator.
Assume that no two passengers are allowed to exit at the same floor.
The first passenger could choose from any of the floors.
However, the second passenger would not be able to choose the same floor as the first passenger. Thus, the second passenger would have to choose from only floors.
Likewise, the third passenger would have to choose from only floors.
Thus, under the requirement that no two passenger could exit at the same floor, there would be only unique ways for these two passengers to exit the elevator.
By the assumption that the choices of the passengers are independent and uniform across the floors. Each of these
combinations would be equally likely.
Thus, the probability that the chosen combination satisfies the requirements (no two passengers exit at the same floor) would be:
.