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1. Domain is all real numbers except ____

2. Range is all real numbers except ____
3. Interval of decrease is all real numbers except ____
4. Horizontal asymptote: ____
5. Vertical asymptote: ____
6. Hole at x = ____

1. Domain is all real numbers except ____ 2. Range is all real numbers except ____ 3. Interval-example-1
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User Soenhay
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1 Answer

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1. The domain is all real numbers except x = 3, since at x = 3, the denominator becomes zero, and the function becomes undefined.

2. The range is all real numbers except y = 4, since the function can take any other real value.

3. The function is continuous and decreasing on the intervals (-∞, 3) and (3, ∞), so the interval of decrease is all real numbers except x = 3.

4. The horizontal asymptote is y = 0, since as x approaches positive or negative infinity, the function approaches zero.

5. The vertical asymptote is x = 3, since the denominator becomes zero at x = 3, and the function becomes undefined.

6. There is a hole in the graph at x = 3, since the function is undefined at this point. However, the hole can be "filled" by simplifying the function to (2x - 6)/(x - 3) and noting that the factor (x - 3) cancels out, leaving the function equal to 2 for all x not equal to 3.
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User Mike Braun
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