Chapter 1.8, Problem 1CYU

To determine

To identify the function as linear or non-linear, estimate and interpret the intercepts of graph.

Explanation of Solution

Given:

Here, x - axis represents Time since Opening Bell in hours

y - axis represents Price Variation (points)

Linear or Non-Linear: The graph is a straight line but the rate of change is different in different interval.

Hence, the graph is non-linear.

y - intercept: The graph intersects the y -axis at the point (0, 0).

So, the y - intercept of the graph is 0. This means, that the initial price variation was 0 points.

x - intercept: The graph intersects the x -axis at the point (0, 0), (3, 0) and (4.5, 0).

So, the x - intercept of the graph is 0, 3 and 4.5. This means, that the price variation becomes 0 points at 0, 3 and 4.5 hours.

Positive or Negative:

From above figure, it is clear that, the graph is above x -axis from x = 0 to x = 3 and x = 4.5 and beyond. So, the graph is positive in that region.

Whereas from x = 3 to x = 4.5 the graph is below x -axis. So, the graph is negative in that region.

Relative Extrema:

The relative extrema are shown in below figure.