Q. 3 ACYPExpert-verified
Graph the function, and compare to the parent graph. State the domain and range.
The domain of the given function is and the range is
Parent graph: The simplest form of the given function is called the parent function of that function and the graph of the parent function is called parent graph.
Domain: The set of all possible values for which given function defined is called domain.
Range: The set of all possible values of the given function is called range.
The given function is:
In order to graph a function, find few co-ordinates by substituting values of ‘’ and find finding the respective values of ‘'.
|Values of ‘||Values of ‘’|
Plot these co-ordinates on a coordinate plane and join those points to get the required graph.
The parent function of is the simple square root function.
The graph of parent function is given below.
Note: Since the parent function is just used for comparison, it is graphed using graphing calculator.
The graph is obtained by parent function is subtracted by ‘4’.
Therefore, the graph is translated(shifted) downward by 4 units from the origin, on comparing with the parent graph .
Since ‘’ is inside the root, the values inside the root must be positive.
Therefore, values of is all positive real numbers including zero.
That is, .
In the square root of x is subtracted by ‘4’.
As square root is always positive, the least value it takes is zero.
Find the starting value of the function by substituting in .
Also, in , coefficient of is 1, which is positive.
Therefore, takes all the real values greater than or equal to ‘’.
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