1) Domain: All real numbers.
Range: All real numbers.
it is a function.
2) Domain: All real numbers.
Range: y ≥ 0
it is a function.
3) Domain: x ≥ 0
Range: All real numbers.
it is a not function.
How to find the domain and the range?
For the domain we need to look at the horizontal range and see in which interval is the graph, and for the range we need to look at the vertical axis. Finally, to know if the relation is a function we can use the vertical line test.
If we can draw a vertical line that intercepts the graph more than once, then it is not a function.
1) This is a linear function, both domain and range are the set of all real numbers.
2) This is an absolute value function, the domain is the set of all real numbers, the range is the set of all values larger than the vertex, which is at y = 0, so the range is:
y ≥ 0.
3) Another absolute value, but this is not a function. Here the range is the set of all real numbers, and the domain is the set of x values equal or larger than zero:
x ≥ 0