Monica built a remote-controlled, toy airplane for a science project. to test the plane, she launched it from the top of a building. the plane traveled a horizontal distance of 50 feet before landing on the ground. a quadratic function which models the height of the plane, in feet, relative to the ground, at a horizontal distance of x feet from the building is shown.

since the domain represents the airplane while it was in the air, the values of the domain should be restricted to the interval [, ].

[0,50]

Step-by-step explanation:

The function takes from value the distance from the plane to the building, and returns the height of the plane at that point in feets. Assuming that the plane goes always down, it will always be up to the height of the building. Note that the horizontal distance the plane travels at any point is equivalent to the distance of the plane with the building at that point, because the building is perpendicular to the ground. So, at the end of the travel the plane will be 50 feets away from the building. SInce it starts at 0 distance, then the domain of the function is [0,50]

find the magnitude of the trig term  

csc

(

x

)

−

1

by taking the absolute value of the coefficient.

1

find the lower bound of the range.

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y

=

−

2

find the upper bound of the range.

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y

=

0

the range is  

y

≤

−

2

or  

y

≥

0

.

(

−

∞

,

−

2

]

∪

[

0

,

∞

)

{

y

|

y

≤

−

2

,

y

≥

0

}

step-by-step explanation:

what is the original number? you forgot to add it.