Question

For the equation (x - 3)² + (y + 2)² = 5r², find the following information:

Domain:
Range:

Answer 1

The equation represents a circle and the domain and range are the intervals of possible x and y values within the circumference of the circle with center at (3, -2) and radius √(5r²).

Step-by-step explanation:

The equation (x - 3)² + (y + 2)² = 5r² represents a circle on the Cartesian coordinate system with a center at (3, -2) and a radius of √(5r²). The domain and range of a circle are all the possible x and y values that points on the circumference can have, respectively.

For the domain (the possible x-values), since the radius extends to the left and right from the center, the domain is all real numbers such that x is between (3 - √(5r²)) and (3 + √(5r²)). For the range (the possible y-values), since the radius extends up and down from the center, the range is all real numbers such that y is between (-2 - √(5r²)) and (-2 + √(5r²)).

If r is a constant value, then the domain and range are specific intervals. However, if r can vary, then we must consider all possible values of r; this would affect the size of the circle and thus the intervals for domain and range.