Which statements about the graph of f(x) = √x are true? Select all that apply.

Question

Here are the choices.

A. The domain is restricted to x > 0.

B. The range is restricted to f(x) > 0.

C. The x-intercept is 0.

D. The y-intercept is 0.

E. The graph is increasing for all values in the domain of f.

Answer 1

C, D, and E are correct

A. The domain is restricted to x > 0 - The domain should be x ≥ 0 because the square root of a negative number is imaginary, but the square root of 0 is real.

B. The range is restricted to f(x) > 0. - The range should also be f(x) ≥ 0 since the f(0) = √0 = 0. Technically, the square root of x would provide a positive and negative result, but that would cause conflict when graphing since a function needs to pass the vertical line test. So as far as graphing a function, the range is f(x) ≥ 0.

C. The x-intercept is 0. - True since the graph goes through the point (0,0).

D. The y-intercept is 0. - True since the graph goes through the point (0,0).



E. The graph is increasing for all values in the domain of f. - True since as x gets larger, so does its square root.

Answer 2

I would say that the correct answers are A, C & D.

f(x) =  √x is not a function since the answers can be either positive or negative.

To convert this into a bona-fide function one would have to write

f(x) = +I√x I or f(x) = -√x I