Question

Sketch the region in the plane defined by each of the following equations, where ⌊x⌋ is the greatest integer function. 1.2. 1 (a) [3] [x]² +⌊y∣ ²=1

Answer 1

To sketch the region defined by the equation [3] [x]² + ⌊y∣ ²=1, we need to consider the possible values for x and y that satisfy the equation.

Step-by-step explanation:

The equation you provided, [3] [x]² + ⌊y∣ ²=1, involves the greatest integer function, ⌊x⌋. To sketch the region defined by this equation, we need to consider the range of possible values for x and y that satisfy the equation.

Let's start by looking at the x-values. Since [x] represents the greatest integer less than or equal to x, the values of x that satisfy the equation are integers in the range (-1, 0, 1).

Next, let's consider the y-values. The equation can be rewritten as [3] [x]² = (1 - ⌊y∣ ²). Since the greatest integer function ⌊y∣ ² will always be a non-negative integer or zero, we have two possibilities for this term: it can either be equal to 1 or equal to 0. This means that the possible values for y are (-1, 0) and (0, 1).