Graph y = square root of 4-x^2

Problem

y=√(,4−x2)

Solution

1. Identify the domain of the function by ensuring the expression under the square root is non-negative.

4−x2≥0

x2≤4$$$$−2≤x≤2

2. Square both sides of the equation to identify the shape of the curve.

y2=4−x2

3. Rearrange the equation into the standard form of a circle.

x2+y2=4

4. Determine the geometric properties of the equation, which represents a circle centered at (0,0) with a radius of r=√(,4)=2

5. Restrict the graph based on the original function y=√(,4−x2) Since the principal square root is non-negative, y≥0

6. Conclude that the graph is the upper semicircle of x2+y2=4

Final Answer

y=√(,4−x2)* is the upper semicircle of *x2+y2=4* where *y≥0

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