Kstands for a whole number.
k+7 is greater than 100
k-7 is less than 90
find all the numbers that k could be

If (k+7) is greater than 100, then,
k+7 > 100
k+7-7 > 100-7
k > 93

If (k-7) is less than 90, then,
k-7 < 90
k-7+7 < 90+7
k < 97

Combine the two solutions k > 93 and k < 97 to get this compound inequality: 
93 < k < 97

The number k is between 93 and 97. We are not including 93. We are not including 97.

If k is a whole number, then this is the set of possible values for k: {94, 95, 96}

94, 95, or 96

  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.

f(-2) = -3f(1) = 6 . . . estimated from f(x) = (x+2)^2-3, which matches points on the graph (-1,-2) and (0, 1)

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

the table tells us

g(-2) = 1g(1) = 31

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).

Where is the diagram