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Inclusive [ ] equal to Exclusive ( ) not equal Left (small) 2 x 3 x4 2 x All Real Numbers All Real Numbers except 1 Right (big) [-2, (-2, 3] ∞) (-∞, 4) (-∞ , (-∞ 1) U,∞) (1, ∞) Union (U) means or. So we are It goes left to, forever right choosing everything negative Infinity and negative Equal usefrom [and ] infinity forever, it’s negative infinity up toso1,with and are always (then ). from 1 to Not to,we useare ( ) taking out infinity toequal the But left, positive positive infinity. Since goes left forever, we circle infinity to the right. one. It’s itlike if we have an open negative infinity. on use a number line. 0 Basic Domains 1 x 1 Denominator cannot equal zero. x 1 0 x 1 All quantities inside square roots must be greater than or equal to zero. So x 1 All other x' s work, so the domain is all real To find where the denominator can’t be zero, make it equal zero and solve. numbers except - 1 D: (-∞ , -1) U (-1, ∞) 0 Basic Domains 4 x Denominator cannot equal zero. 4 x 0 x x All quantities inside square roots must be greater than or equal to zero. 4 x Make quantity inside square root bigger than or equal to zero and solve. D: (-∞ , 4] 0 f Find the domain of g remember, denominato r can' t equal 0 1) Find the domains of each 2) Find where they overlap f ( x) 4 x 4 x 0 g ( x) x 2 4 (,) x x 4 x ( ,4] 3) Find where denominator equals zero. 4) Write the domain, a number line may help. We are taking out -2 and 2. D:2)(-∞ , 4]4] D: (-∞ , -2) U (-2, U (2, 0 x2 4 0 x 2 f Find the domain of g remember, denominato r can' t equal 0 1) Find the domains of each 2) Find where they overlap f ( x) 4 x 4 x 0 g ( x) x 1 x 1 0 x x 4 x ( ,4] 1 1 x 1 [1, ) 3) Find where denominator equals zero. 4) Write the domain, a number line may help. 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. We are taking out 1 D: (1, [1 , 4] 4] 0 x 1 0 x 1