Question

Which statement is true about the function f(x)= Vx?

Answer 1

Answer:

The statement "the range of the graph is all real numbers greater than or equal to 0" is true.

Step-by-step explanation:

As the function is given by

                                             

As we know that the domain is the set of all possible input values or all  x -values that a function passes through.  In other words, domain consists of all the possible input values shown on the x-axis.

Range is the set of all y-values that a function passes through. In other words, range consists of all the possible output values shown on the y-axis.

For the given function

                                       

The domain of the given function  

The domain of  can also be written as: {x | x ≥ 0}

It means the domain of the graph of this function is all real number greater than or equal to 0.

The domain of the graph of this function can not be less than zero, because if we put any negative real number in this function, it would make the the function undefined.

Please check the attached graph as shown in figure a, to visualize the domain and range of  

From the graph.

it is visible that the range of the given function  

The range of  can also be written as: {y | y ≥ 0}

In other words, for every input value in the domain of this function, the range of   will be all real numbers greater than or equal to 0. Please see the attached graph as shown in figure a.

So, from the entire discussion, we can safely say that the statement "the range of the graph is all real numbers greater than or equal to 0" is true.