Question

Each graph shows a relation. The first and second numbers of each ordered pair in the relation are members of the set of real numbers. In each case, find the domain and range and determine whether the relation is a function.

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Answer 1

Answers:

• Domain:
  `-2 \le \text{x} \le 2`
• Range:
  `-2 \le \text{y} \le 2`
• The relation is not a function

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Step-by-step explanation:

The domain is the set of possible x values. The left-most point occurs when x = -2, while the right-most point is when x = 2. Therefore, x is between -2 and 2 in which we write
`-2 \le \text{x} \le 2`. Both endpoints are included.

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The range is the set of possible y values. The possible y values are in the interval
`-2 \le \text{y} \le 2` since y = -2 is the smallest y can get, and y = 2 is the largest it can get. Visually we look at the lowest and highest points respectively to find the span of y values.

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This relation is not a function because it fails the vertical line test.

It is possible to pass a single vertical line through more than one point on the curve. For example, the vertical line through x = -1 goes through the points (-1,1) and (-1,-1)

Phrased another way: The input x = -1 leads to more than one output.

A function is only possible if each input in the domain leads to exactly one output.