Question

What is the average rate of change of f(x), represented by the graph, over the interval [-1, 1]? and my answers are

Answer 1

Answer: Choice C) 5

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Explanation:

Step 1) Draw a vertical line through -1 on the x axis. This vertical line crosses through the point (-1,-5) which is a point on the hyperbola.

Step 2) Draw a vertical line through 1 on the x axis. This line crosses the hyperbola at (1,5).

Step 3) Find the slope of the line through the two points (-1,-5) and (1,5) using the slope formula

m = (y2 - y1)/(x2 - x1)
m = (5 - (-5))/(1 - (-1))
m = (5 + 5)/(1 + 1)
m = 10/2
m = 5

The slope of the line is 5. This is the same as saying the average rate of change is 5. The average rate of change is over the interval [-1,1] which is the same as the interval -1 <= x <= 1

Note: writing "<=" without quotes means "less than or equal to".