Question

Determine if the function has a constant or a variable rate of change over the interval provided. Explain or show how you know.

This answer has not been graded yet.
x
-8
-7
-6
-5
-4
-3
-2
-1
y
80
63
48
35
24
15
8
3

Answer 1

the function represented by the given values has a variable rate of change over the provided interval.

Explanation:

To analyze a function's rate of change, we examine the y-values for different x-values in the given interval:

Between x = -8 and x = -7:

Rate of change = (y2 - y1) / (x2 - x1)

(63 - 80) / (-7 - (-8) = 17

Between x = -7 and x = -6:

Rate of change = (y2 - y1) / (x2 - x1)

(48 - 63) / (-6 - (-7) = 15

Between x = -6 and x = -5:

Rate of change = (y2 - y1) / (x2 - x1)

(35 - 48) / (-5 - (-6) = 13

Between x = -5 and x = -4:

Rate of change = (y2 - y1) / (x2 - x1)

(24 - 35) / (-4 - (-5) = 11

Between x = -4 and x = -3:

Rate of change = (y2 - y1) / (x2 - x1)

(15 - 24) / (-3 - (-4)= 9

Between x = -3 and x = -2:

Rate of change = (y2 - y1) / (x2 - x1)

(8 - 15) / (-2 - (-3) = 7

Between x = -2 and x = -1:

Rate of change = (y2 - y1) / (x2 - x1)

(3 - 8) / (-1 - (-2)= 5

The function has a variable rate of change within the given interval, as the calculated rates of change are not consistent across the x-values.

I have a strong feeling this is correct :)