What are the domain and range for #x^2 + 9y^2 = 25#?
2 Answers
Explanation:
The domain represents those
We can see this in practice by solving the above equation for
We start with the domain. Since there is a square root involved, we know that the square roots of negative values is not defined in the real number system. Thus, the radicand (the term inside of the square root) must be strictly non-negative:
The range comes from examining the possible values that the expression for
Putting these together:
Side Note
You could visually see this by recognizing the original relation given is the equation for an ellipse with center at (0,0) and a semi-major axis of 5 and a semi-minor axis of
graph{x^2+9y^2=25 [-6, 6, -2.5, 2.5]}
Explanation:
The major axis
the minor axis
Domain is
Range is