Problem 66 - College Algebra

Question

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

Step-by-Step Solution

Answer

A \([-20,2,1]\) by \([-4,5,0.5]\) viewing rectangle means that the graph is being viewed within a window with x-values ranging from -20 to 2, scaled by 1 unit per mark, and y-values ranging from -4 to 5, scaled by 0.5 units per mark.

Step 1: Interpret the x parameters

The parameters for the x-axis are given as \([-20,2,1]\). This means that the minimum x-value (the leftmost point on the x-axis) is -20, the maximum x-value (the rightmost point on the x-axis) is 2, and the units between each tick mark on the x-axis is 1.

Step 2: Interpret the y parameters

The parameters for the y-axis are given as \([-4,5,0.5]\). This means that the minimum y-value (the bottommost point on the y-axis) is -4, the maximum y-value (the topmost point on the y-axis) is 5, and the units between each tick mark on the y-axis is 0.5.

Step 3: Combine the interpretations

So the given viewing rectangle \([-20,2,1]\) by \([-4,5,0.5]\) indicates a viewing window for a graph where the x-values range from -20 to 2 with a scale of 1 unit per tick mark, and the y-values range from -4 to 5 with a scale of 0.5 units per tick mark. This defines the observable area for the plot of function.