Which of the following is true about the graph of y = √x?

For any function involving a square root, the expression under the root must be non-negative for the output to be a real number — this restriction on valid inputs is called the domain of the function, and it directly shapes which part of the graph actually exists.

For y = √x, the quantity under the root is x itself, so x must be non-negative for y to be real. As x increases from this starting point, the value of y increases too — the graph rises steadily from the origin rather than curving back on the other side of the y-axis.

• The secant slope from x = 0 to x = 1 is (1 − 0)/(1 − 0) = 1, whereas from x = 1 to x = 4 it is (2 − 1)/(4 − 1) = 1/3; the different slopes rule out a straight line.

• y at x = 1 versus x = 9 gives 1 versus 3 — the value grows rather than shrinks.

• Testing x = −4 in the same rule does not give a real output, confirming the restriction to non-negative x.

So among the four descriptions, only the domain restriction (x ≥ 0) correctly describes this graph.