By the Triangle Inequality Theorem, if two sides of a triangle have lengths of 6 and 13, what are the possible lengths of the third side?

A) 7 < x < 18
B) 7 < x < 19
C) 8 < x < 18
D) 8 < x < 19

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).