Answer:
- is a function
- domain: [-6, 2]
- range: [-4, 0]
Explanation:
You want to know if the graph of the semicircle centered at (-2, 0) with radius 4 extending below the x-axis is a function. You also want to know its domain and range.
Function
The graph passes the vertical line test. That is, no vertical line intersects the graph in more than one place. That means the relation is a function.
Domain
The domain of the function is the horizontal extent of the graph. The solid dots at the extreme points of (-6, 0) and (2, 0) indicate those points are part of the domain. The domain also includes all x-values between them. In interval notation, the domain -6 ≤ x ≤ 2 is written as ...
[-6, 2]
Range
The range is the vertical extent of the graph. The semicircle extends from a low point of (-2, -4) to high points on the x-axis. Thus its range is -4 ≤ y ≤ 0, written in interval notation as ...
[-4, 0]
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Additional comment
The brackets used in interval notation are square brackets if the end points are included in the interval. Otherwise, they are round brackets (parentheses).