I'd rather not take your points but here's your answer, 1. False. The function f(x) = √x represents the square root function. The square root of a number can be positive or negative, so f(x) can take on positive values.
2. True. Since the square root of a number cannot be negative, f(x) is never negative.
3. True. The number 0 is in the domain of f because we can take the square root of 0, which is 0.
4. True. The number 1 is in the domain of f because we can take the square root of 1, which is 1.
5. False. Negative real numbers are not in the domain of f. The square root of a negative number is not a real number.
6. True. All positive real numbers are in the domain of f. We can take the square root of any positive number and obtain a real number.
7. False. The function f(x) can be zero when x is zero. The square root of 0 is 0, so f(x) can be zero.
To help visualize the graph of f(x) = √x, imagine a graph starting at the origin (0,0) and then curving upward to the right. It will pass through the point (1,1) and continue on in the positive x-direction. The graph will never dip below the x-axis since the square root function is never negative.
Please note that the graph of f(x) = √x does not extend to the left of the y-axis, as taking the square root of a negative number is not defined in the real number system.