Changing the Graphing Window

5.11.1 Changing the Graphing Window

5.11.1 • Changing the Graphing Window

Warm Up

Here is a graph of a function $f (x) = 400 \cdot (0.2)^{x}$ .

A graph with x-axis labeled x and y-axis labeled y. The x-axis is labeled by tens from zero to 40 with additional grid marks on even numbers. shows a curve rapidly decreasing from y = 1000 near x = 0, then leveling off close to y = 0 as x approaches 2.

Identify the approximate graphing window shown.

Compare your answer:

$0 < x < 44$ and $0 < y < 1, 100$ or equivalent

2. Suggest a new graphing window that would:

a. make the graph more informative or meaningful.

b. make the graph less informative or meaningful.

Compare your answer:

a. $0 < x < 10$ and $0 < y < 450$ . This window would include $x$ -values where meaningful changes happen and exclude the parts where the changes are very small. The $y$ -values are limited to values that matter, between 0 and 400, allowing us to see more clearly the changes in that range.

b. $- 10 < x < 80$ and $10 < y < 100$ . This window would show a lot of useless $x$ -values and cut off the $y$ -values at 100, which would make the behavior of the function when 𝑥 is between 0 and 1 very difficult to observe.