Given h of x equals negative 2 times the square root of x minus 3 end root, which of the following statements describes h(x)?
1 answer:
Answer:
The function h(x) is decreasing on the interval (3, ∞).
Step-by-step explanation:
Please take a look at the attached image.
You will see a graph of the given function h(x) = -2. The function is decreasing.
The function starts at 3 and starts to go towards negative infinity on the x-axis. Therefore the function is decreasing on the interval (3, ∞).
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Step-by-step explanation:
The vertex form of the equation for a parabola is given by
where (h, k) are the coordinates of the parabola's vertex. Since the vertex is at (1, -6), we can write the equation as
Also, since the parabola passes through (4, -7), we can use this to find the value for a:
or
Therefore, the equation of the parabola is
Answer:
The area function is
.
The domain and range of A is and
.
Step-by-step explanation:
The given length of fencing is .
Let the length and width of each pen be and
respectively as shown in the figure.
As there are 3 pens, so, the total area,
From the figure the total length of fencing is .
Here, for a significant area for the animals, as well as
as
and
are the sides of ben.
From the given value:
Now, from equation (i)
This is the required area function in the terms of variable .
For the domain of area function, from equation (ii)
[as y>0]
So, the domain of area function is .
For the range of area function:
As or
, then
[from equation (i)]
Now, differentiate the area function with respect to .
Equate to zero to get the extremum point.
Check this point by double differentiation
As, , so, point
is corresponding to maxima.
Put this value back to equation (iii) to get the maximum value of area function. We have
Hence, the range of area function is .
