Answer
See below:
Work Step by Step
(a)
By the definition of a function,
“There should not be any single x in its domain, which has more than one value of the function.”
It can be concluded that if the vertical line is drawn on the graph, and if more than one point of intersection is observed, then that graph will not be a graph of the function.
In the given above graph, it can be easily observed that vertical line intersects only at a single point.
Therefore, the height of eagle is a function of time.
Hence, the height of eagle at any time “t” is a function of time.
(b)
From the above plot of the graph of eagle’s height in terms of height, it can be easily seen that
At\[t=15\] seconds, the graph touches the x-axis.
It means the value of the height of eagle is zero at that time.
Therefore, the value of\[f\left( 15 \right)=0\], and at \[t=15\]seconds, the eagle was on the ground.
Hence, the value of\[f\left( 15 \right)=0\], and at \[t=15\]seconds, the eagle was on the ground after 15 seconds.
(c)
From the above plot of the graph of eagle’s height in terms of height, it can be easily seen that
At\[t=0\], in seconds, it comes close to ground and after \[t=15\]seconds it again rises to the sky.
Only at\[t=0\], it is at the height \[45\text{ m}\], which is the maximum height from the ground.
Hence, the maximum height of eagle is\[45\text{ m}\]at\[t=0\].
(d)
From the above plot of the graph of eagle’s height in terms of height, it can be easily seen that
In time interval\[t=0\]to 3 seconds, there was no change in height from the ground.
In time interval\[t=3\] to \[t=12\] seconds, the height of eagle is descending from the ground.
Therefore, the eagle is descending during the interval\[t=3\]and\[t=12\].
Hence, the eagle is descending during interval t = 3and t = 12.
