Question

The curve is labeled f left parenthesis x right parenthesis. The curve begins at the plotted point left parenthesis 0 comma 0 right parenthesis then passes through the plotted points left parenthesis 1 comma 1 right parenthesis and left parenthesis 4 comma 2 right parenthesis. The curve continues through approximately left parenthesis 5 comma 2.25 right parenthesis.

Use the average rate of change to describe the graph of f(x) over the interval [1,4] .

(1 point)
Responses

The average rate of change is 3.
The average rate of change is 3.

The average rate of change is 1 .
The average rate of change is 1.

The average rate of change is 13 .
The average rate of change is Start Fraction 1 over 2 End Fraction .

The average rate of change is −13 .
The average rate of change is negative Start Fraction 1 over 2 End Fraction .

Answer 1

Average rate of change = (f(4) − f(1)) / (4 − 1) = (2 − 1) / 3 = 1/3.

So f increases on [1,4] at an average rate of 1/3 unit in f for each 1 unit in x.