Question

Use the table of the function f(x) = x4 - 2x3 to answer this question.

x f(x)
-1 3
0 0
1 -1
2 0
3 27
What is the average rate of change from x = -1 to x = 1?
-2
0
2
4

Answer 1

Average rate of change from x = a to x = b is given by the formula:
\[
\frac{f(b)-f(a)}{b-a}
\]Average rate of change from x = -1 to x = 1 is given by:\[
\frac{f(1)-f(-1)}{1-(-1)} = ?
\]

Answer 2

What does the f in this equation stand for? Do I choose any function of x from the chart?

Answer 3

f(x) is the function.
f(b) is the value of the function when x = b

You are given a table of x values and the corresponding f(x) values:
x f(x)
-1 3 when x = -1, f(-1) = 3
0 0
1 -1 when x = 1, f(1) = -1
2 0
3 27
\[
\frac{f(1)-f(-1)}{1-(-1)} = \frac{-1-3}{1+1} = \frac{-4}{2} = -2
\]