Problem 53 - College Algebra

Question

What does a \([-20,2,1]\) by \([-4,5,0.5]\) viewing rectangle mean?

Step-by-Step Solution

Answer

The \([-20,2,1]\) by \([-4,5,0.5]\) viewing rectangle means that the viewing area for the graph has been set to range from -20 to 2 (inclusive) on x-axis with each tick representing 1 unit, and from -4 to 5 (inclusive) on the y-axis with each tick representing 0.5 units.

Step 1: Understand and Narrow Down the Given Vectors

Given are two vectors, \([-20,2,1]\) and \([-4,5,0.5]\). As per the structure of a viewing rectangle, the first vector, \([-20,2,1]\), pertains to the x-axis while the second vector, \([-4,5,0.5]\), pertains to the y-axis. From this, after analyses, the x-axis range is from -20 to 2 with each tick on the x-axis representing 1 unit, while the y-axis range is from -4 to 5 with each tick on the y-axis representing 0.5 units.

Step 2: Visualizing the Viewing Rectangle

With the range and scale of the x and y axes established, a mental image of the viewing rectangle can be formulated. The result will be a rectangle that starts from -20 on the x-axis and ends at 2 while on the y-axis it starts from -4 and ends at 5. Further, the scaling on the x and y axis means plotting of data would take into account these intervals.