Question

The function y, equals, f, of, xy=f(x) is graphed below. Plot a line segment connecting the points on ff where x, equals, minus, 5x=−5 and x, equals, minus, 3, .x=−3. Use the line segment to determine the average rate of change of the function f, of, xf(x) on the interval minus, 5, is less than or equal to, x, is less than or equal to, minus, 3, .−5≤x≤−3. -1 and 15 for values of -5 and -3

y =? x=? average rate of change?

Answer 1

If f(−5) = −1 and f(−3) = 15, the two points are (−5, −1) and (−3, 15).

Average rate of change = [f(−3) − f(−5)] / [−3 − (−5)]
= (15 − (−1)) / 2
= 16 / 2 = 8.

The secant line through those points has slope 8. Using point (−5, −1):
y + 1 = 8(x + 5) ⇒ y = 8x + 39.

So:
- endpoints: (−5, −1) and (−3, 15)
- average rate of change: 8
- secant line: y = 8x + 39.