O 2x 3 is 2x 3 when 2x 3 0 therefore when therefore

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Unformatted text preview: 2 ; −1 should be an acceptable root of the absolute value equation. Check. Answer: x = −1 or x = 4 exercise: Solve | 2x − 3 | = x algebraically. [Answer: 1 or 3] Unit 6: Day 3 notes - Absolute Value Equations Page 3 of 4 example: Solve | 2x − 3 | = 4x algebraically. o | 2x − 3 | is 2x − 3 when 2x − 3 ≥ 0 . Therefore, when Therefore if x ≥ 3 2 x≥ 3 2 2x − 3 = 4x , the equation will become 3 x =−2 Solve this equation. This root is the result from an equation that is valid only if x ≥ 3 2 3 ; −2 cannot be acceptable root of the absolute value equation. It must be an extraneous root. Check; it does not satisfy the absolute value equation. o | 2x − 3 | is −(2x − 3) when 2x − 3 < 0 . Therefore if x < 3 2 x< 3 2 −(2x − 3) = 4x , the equation will become Solve this equation. x= This root is the result from an equation that is valid only if x < 3 2 ; 1 2 1 2 should be an acceptable root of the absolute value equation. Check. Answer: x= 1 2 example: Solve | 2x − 3 | = 4x graphically. o Graph o y = | 2x − 3 | and Answer: x= 1 2 y = |2x − 3| 4 y = 4x ( 1 ,2) is the only point on both graphs. 2 It's x-coordinate is y . 1 2 Note where the extraneous root is on the graphs. 2 y = 4x -2 0 2 x Unit 6: Day 3 notes - Absolute Value Equations Page 4 of 4 exercise: Solve | 2x − 3 | = −x algebraically. [Answer: No solution] exercise: Solve | x2 − 9 | = 3x − 9 algebraically. [Answer: 0 or 3] exercise: A packaging company rejects any juice pack that contains an amount of juice that differs from the labelled amount by more than 5 millilitres. A juice pack having 202 mL is acceptable. Write an absolute value equation that can be used to determine the greatest and least amount of juice that might be acceptable. [Answer: | x − 202 | = 10] EXTENSION Solve |x+1| + |x−3| = 6 algebraically. [Answer: −2 or 4] EXTENSION Solve | 2x − 3 | >5 algebraically and graphically. [Answer: x < −1 or x > 4] PRE-CALCULUS 11 Unit 6 – Day 4: RECIPROCAL FUNCTIONS (Part 1) RECIPROCAL FUNCTIONS A reciprocal function is a function that is the reciprocal of some other function. y = 1 is the reciprocal function of y = f (x) . f ( x) example: Compare the basic reciprocal function with the basic linea...
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