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 xcoordinate 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] PRECALCULUS 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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 Fall '11
 Aytona
 Calculus, PreCalculus

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