The answer key says [0, infinity). Please describe and show to me the process of finding this. Finding the range of a function will be a question on my midterm tomorrow.
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Consider the parabola x = y^2
The curve divides the xy-plane in two regions
Domain of the function is the region D containing the symmetry axis of the parabola
D = {(x,y)∈ℝ² | x ≥ y^2}
The range is the set ℝ⁺ of all positive real values, included zero
Indeed for any k ≥ 0 there exist (x,y) such that √(x - y^2) = k
x - y^2 = k^2
all the points of the parabola having equation
x = y^2 + k^2
The curve divides the xy-plane in two regions
Domain of the function is the region D containing the symmetry axis of the parabola
D = {(x,y)∈ℝ² | x ≥ y^2}
The range is the set ℝ⁺ of all positive real values, included zero
Indeed for any k ≥ 0 there exist (x,y) such that √(x - y^2) = k
x - y^2 = k^2
all the points of the parabola having equation
x = y^2 + k^2