Which of the following correctly uses absolute value to show the distance between −70 and 13? (5 points)

−70 − 13| = |−83| = −83 units
|−70 − 13| = |−83| = 83 units
|−70 + 13| = |−57| = 57 units
|−70 + 13| = |−57| = −57 units

B

Step-by-step explanation:

First of all, distance cannot be negative so you eliminate answers A and D immediately.

Now to find the distance between a negative number and a positive number, you either have to take the absolute value of the negative number (to turn it positive) and add it to the positive or take the absolute value of the positive number subtracted by the negative number.

Basically, you're doing this because it compensates for the distance between the negative number and 0.

The only answer choice that is consistent with these terms is B.

  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).