Question

Graph the set defined by the following cross products

involving interval notations : [2,5]×[-3,4]

Answer 1

To graph the set defined by the cross product [2,5]×[-3,4], plot and shade a rectangle with vertices at (2,-3), (2,4), (5,-3), and (5,4) on the Cartesian coordinate system.

Step-by-step explanation:

The student's question involves graphing the Cartesian product of two intervals, [2,5]×[-3,4]. This represents a set of ordered pairs, where the first element comes from the interval [2,5] and the second element comes from the interval [-3,4]. In order to graph this, you would need to plot a rectangle on the Cartesian coordinate system with corners at the points (2,-3), (2,4), (5,-3), and (5,4). This rectangle represents all the possible ordered pairs formed from the two intervals.

To graph this set:

1. Draw a Cartesian coordinate system with both x and y axes scaled appropriately to include the intervals [2,5] and [-3,4].
2. Mark the interval [2,5] on the x-axis.
3. Mark the interval [-3,4] on the y-axis.
4. Draw straight lines to connect (2,-3) to (2,4) and (5,-3) to (5,4) vertically.
5. Draw straight lines to connect (2,-3) to (5,-3) and (2,4) to (5,4) horizontally.
6. Shade the interior of the rectangle to represent all the points in the set [2,5]×[-3,4].