Square root functions (for example: y= √x) is defined as the function where the output ‘y’ when multiplied by itself (squared) gives the input ‘x’. The symbol ‘√’is called the ‘radical symbol’ and the general form of any square root function is given by:
The general form of any square root function is given by:
The domain of a square root function is not all real numbers because of the fact that we have a square root right there!
To get real solutions, no negative number is allowed under the square root; hence the domain condition becomes:
Example:Find the domain of y = √(x+5)
So, set it according to the above condition always and get
-> x+5 > 0 -> x > -5
Interval notation: [-5, infinity)
The constants ‘a’, ’c’ and‘d’ transform the graph of the parent function horizontally and vertically.
Example: Graph the function: y= √(x-4) – 2
Domain: x- c>= 0 -> x>= 4
Then fill the table with values based on the domain.
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