Question

Given that a function, g, has a domain of -20 ≤ x ≤ 5 and a range of -5 ≤ g(x) ≤ 45 and that g(0) = -2 and g(-9) = 6, select the statement that could be true for g.

A.
g(-4) = -11
B.
g(0) = 2
C.
g(7) = -1
D.
g(-13) = 20

Answer 1

Statement D: true, because 20 is within the range of g.

Explanation:

Drawing coordinate axes and marking the points given for x = 0 and x = -9

we see that x: {-9, 0} and g(x) = {6, -2}. These sets are within the domain and range of g(x) as given.

The graph of g(x) cannot be precisely determined from the data given, but do indicate that it is a line or mild curve beginning in the 2nd quadrant, crossing the x-axis between x = 0 and x = -5. Therefore:

Statement A is false because the graph is above the x-axis when x is -4;

Statement B: false because g(0) = -11 is outside the range of g;

Statement C: false because x = 7 is outside the domain of g; and

Statement D: true, because 20 is within the range of g.