Explanation:
the domain is the set or interval of all valid x values.
the range is the set or interval of all valid y values.
1.
domain = {-1, 2, 5}
range = {0, 2, 3, 7}
function : no, because x = -1 has 2 different y values assigned (7 and 2). that violates the definition of a function.
2.
domain = {-3, -2, -1, 1, 4}
range = {-5, -1, 0, 2}
function : yes. every x bake has exactly one y value assigned.
3.
domain = {4, 6, 7}
range = {-1, 2, 3, 5}
function : no, because x = 4 has 2 different y values assigned (2 and 5).
4.
domain = [-3, 3) "3" is not included, hence the empty dot
range = [-4, 5]
function : yes
5.
domain = (-infinity, +infinity) "infinity" is not a possible value, so the limits are not included.
range = [-1, 2]
function : yes
6.
domain = [-2, +infinity)
range = (-infinity, +infinity)
function : no. except for x = -2 all x values have 2 different y values assigned.