| Definition | |x| = x if x ≥ 0; |x| = −x if x < 0. Also |x| = √(x²). |a − b| = |b − a|. (abs.pdf p.1) |
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| Equations | 1. Get |…| alone. 2. |…| = negative ⇒ no solution; RHS with x ⇒ restriction RHS ≥ 0. 3. inside = RHS or inside = −(RHS). 4. Check answers. (abs.pdf p.2) |
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| |A| = |B| | A = B or A = −B (e.g. |x| = |x + 2| ⇒ x = −1) |
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| Graph y = a|x − p| + q | Salient point (p; q). a > 0 ⇒ V, a < 0 ⇒ ⋀. Two straight lines from the salient point. Domain ℝ. (abs.pdf pp.3–6) |
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| Range | a > 0: y ≥ q. a < 0: y ≤ q. |
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| Inequalities* | |u| < k ⇒ −k < u < k. |u| > k ⇒ u < −k or u > k. *Not in abs.pdf; standard rule (Paul’s Online Notes). |
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