Question

What is the domain of the square root function graphed below? 

Answer 1

we know that

the domain of the square root function graphed  is equal to

the interval------> [3,∞)

so

the domain is all  real numbers for $x\geq 3$

and

the range of the square root function graphed  is equal to

the interval------> [1,∞)

so

the range is all  real numbers for $f(x)\geq 1$

therefore

the answer is the option

$x\geq 3$

Answer 2

Domain of a function which allows all values to be in it if for those values the function has defined output. The domain of the plotted function is  $x \geq 3$

What is domain and range of a function?

• Domain is the set of values for which the given function is defined.
• Range is the set of all values which the given function can output.

Since in the given plot, the function starts from 3, and is defined for all values after 3, so it is has domain including 3, and all values after 3.

Thus, domain of given function is

$x = 3\\and\\x > 3$

This can be written in short form as $x \geq 3$

(remember that usually, input values are on x axis(horizontal axis), and output values of the function are on y axis (vertical axis)

Thus,

The domain of the plotted function is

Option D : $x \geq 3$

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