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Left (small)

0. Right (big). Left (small). [ -2, ∞ ). ( -2, 3 ]. ( -∞ , ∞ ). ( - ∞ , 4 ). ( -∞ , 1) U (1, ∞ ).

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Left (small)

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  1. 0 Right (big) Left (small) [-2,∞) (-2, 3] (-∞,∞) (-∞, 4) (-∞, 1) U (1,∞) Union (U) means or. So we are choosing everything from negative infinity up to 1, and then from 1 to positive infinity. But we are taking out one. It’s like if we have an open circle on a number line. It goes left forever and right forever, so it’s negative infinity to the left, positive infinity to the right. Infinity and negative infinity are always with ( ). Since it goes left forever, we use negative infinity. Equal to, use [ ] Not equal to, use ( )

  2. Basic Domains Denominator cannot equal zero. All quantities inside square roots must be greater than or equal to zero. 0 To find where the denominator can’t be zero, make it equal zero and solve. D: (-∞, -1) U (-1,∞)

  3. Basic Domains Denominator cannot equal zero. All quantities inside square roots must be greater than or equal to zero. 0 Make quantity inside square root bigger than or equal to zero and solve. D: (-∞, 4]

  4. 0 • Find the domains of each • Find where they overlap • Find where denominator equals zero. • Write the domain, a number line may help. We are taking out -2 and 2. D: (-∞, 4] D: (-∞, -2) U (-2, 2) U (2, 4]

  5. 0 • Find the domains of each • Find where they overlap • Find where denominator equals zero. • Write the domain, a number line may help. We are taking out 1 You don’t want to change it to 2 on the left. Look at the number line, by changing it to 2, it’s not the same. D:(1, 4] D: [1, 4]

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