MCR3U unit 1.docx

MCR3U unit 1.docx - 1 5 x 3)2 – 4 x 1(6 – x 5 x 3 5 x...

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1. ( 5 x + 3 ) 2 ( 4 x + 1 ) ( 6 – x ) ( 5 x + 3 ) ( 5 x + 3 ) ( 4 x + 1 ) ( 6 x ) 25 x 2 + 30 x + 9 24 x 4 x 2 + 6 x 21 x 2 + 5 x + 15 2. 6 80 + 2 75 8 245 14 108 ¿ 6 16 · 5 + 2 25 · 3 8 49 · 5 14 36 · 3 3 5 ¿ ¿ ¿ 6 ( 4 5 ) + 2 ¿ ¿ 24 5 56 5 + 10 3 84 3 ¿ 80 5 74 3 ( 2 5 4 6 )( 3 3 + 8 2 ) ¿ ( 2 · 3 )( 5 ·√ 3 )+( 2 · 8 )( 5 ·√ 2 )+(− 4 · 3 )( 6 ·√ 3 )+(− 4 · 8 )( 6 ·√ 2 ) ¿ 6 15 + 16 10 24 18 32 12 ¿ 6 15 + 16 10 24 9 · 2 32 4 · 3 ¿ 6 15 + 16 10 24 ( 3 2 )− 32 ( 2 3 ) ¿ 6 15 + 16 10 72 2 3. x ( ¿¿ 2 4 ) · ( x 2 2 x + 1 ) ( x 2 x 6 ) · ( x 2 1 ) ¿ ¿ ( x 3 ) ( x + 1 ) ( x 2 ) ( x 1 ) ¿ x 2 3 x 2 2 Restrictions : x≠ 1 ,x ≠ 1 , x≠ 2 , x≠ 3 2 x 9 x 2 + 15 8 3 x + 5 ¿ 2 x 3 x ( 3 x + 5 ) 8 3 x + 5 ¿ 2 x 3 x ( 3 x + 5 ) 3 x ( 8 ) 3 x ( 3 x + 5 ) 2 x 24 x 3 x ( 3 x + 5 ) Restrictions : x≠ 0

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4. f ( x ) = 6 x 2 + 7 x 3 2 x + 3 ( 3 x 1 ) ( 2 x + 3 x ) 2 x + 3 ¿ 3 x 1 1 ¿ ( 3 x 1 ) g ( x ) = 3 x ( 3 x + 1 ) ( 1 + 9 x 2 ) 9 x 2 + 3 x 1 9 x 2 3 x 1 f ( x ) = 6 x 2 + 7 x 3 2 x + 3 = g ( x ) = 3 x ( 3 x + 1 ) ( 1 + 9 x 2 ) Therefore f ( x ) and g ( x ) are equal. 5. y = ( x + 1 ) 2 8 is a quadratic function y = x 3 is a square root function y = 1 x + 4 is a reciprocal function 6.
• Spring '17
• Quadratic equation, 1 k, ten thousand dollars, f x, 100 thousand dollars, maximum value y

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