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.

Answer 1

I don’t have the picture, so I can’t read the y‑values for x = −5 and x = −3. Here’s how you do it and the formula you’ll use — give me the two y‑values or upload the graph and I’ll compute it for you.

Steps
1. Read the y‑values from the graph:
- A = (−5, f(−5))
- B = (−3, f(−3))

2. Plot A and B and draw the straight line segment joining them.

3. Compute the average rate of change (the slope of that segment):
average rate of change = [f(−3) − f(−5)] / (−3 − (−5)) = [f(−3) − f(−5)] / 2.

Example: if f(−5) = 1 and f(−3) = 5 then average rate = (5 − 1)/2 = 2.

If you tell me the values f(−5) and f(−3) (or upload the graph), I’ll compute the exact number.