Math Unit 1.docx - Total/140 Math Unit 1 2 5 x 3 � −(4 x...

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Total /140 Math Unit 1 1. 5 x + 3 ¿ 2 −( 4 x + 1 )( 6 x ) ¿ ¿ ( 5 x + 3 ) ( 5 x + 3 ) ( 4 x + 1 ) ( 6 x ) ¿ ( 25 x 2 + 15 x + 15 x + 9 ) ( 24 x 4 x 2 + 6 x ) ¿ 25 x 2 + 15 x + 15 x + 9 24 x + 4 x 2 6 + x ¿ 25 x 2 + 4 x 2 + 30 x 24 x + x + 9 6 ¿ 29 x 2 + 7 x + 3 2. a) 6 80 + 2 75 8 245 14 108 ¿ 6 5 × 16 + 2 3 × 25 8 49 × 5 14 3 × 36 ¿ 6 ( 4 5 )+ 2 ( 5 3 )− 8 ( 7 5 )− 14 ( 6 3 ) ¿ 24 5 + 10 3 56 5 84 3 ¿ 80 5 74 3 b) ( 2 5 4 6 )( 3 3 + 8 2 ) ¿ 2 5 ( 3 3 ) + 2 5 ( 8 2 ) 4 6 ( 3 3 ) 4 6 ( 8 2 ) ¿ ( 2 × 3 )( 5 × 3 )+( 2 × 8 ) ( 5 × 2 ) −( 4 × 3 ) ( 6 × 3 ) −( 4 × 8 )( 6 × 2 ) ¿ 6 15 + 16 10 12 18 32 12 ¿ 6 15 + 16 10 12 9 × 2 32 4 × 3 ¿ 6 15 + 16 10 12 ( 3 ) 2 32 ( 2 ) 3
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¿ 6 15 + 16 10 36 2 64 3
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great 3. a) x 2 x 6 x 2 4 ÷ x 2 2 x + 1 x 2 1 ¿ x 2 x 6 x 2 4 × x 2 1 x 2 2 x + 1 ¿ ( x + 2 )( x 3 ) ( x 2 )( x + 2 ) × ( x + 1 )( x 1 ) ( x 1 )( x 1 ) ¿ ( x 3 ) ( x 2 ) × ( x + 1 ) ( x 1 ) ¿ ( x 3 )( x + 1 ) ( x 2 )( x 1 ) ¿ x 2 2 x 3 x 2 3 x + 2 Denominator of each fraction should not be equal to zero, and the numerator of the second fraction should not be equal to zero as well (we cannot divide by zero). ( x 2 0 ) , ( x + 2 0 ) , ( x 1 0 ) , ( x + 1 0 ) x≠ 2, x ≠ 2, x≠ 1, x≠ 1 b) 2 x 9 x 2 + 15 x 8 3 x + 5 ¿ 2 x 3 x ( 3 x + 5 ) 8 3 x + 5 ¿ 2 x 3 x ( 3 x + 5 ) 3 8 3 x ( 3 x + 5 )
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¿ 2 x −( 3 x × 8 ) 3 x ( 3 x + 5 ) ¿ 2 x 24 x 3 x ( 3 x + 5 ) ¿ 22 x 3 x ( 3 x + 5 ) ¿ 22 3 ( 3 x + 5 ) ¿ 22 9 x + 15 3 x≠ 0,3 x + 5 0 x≠ 0,3 x ≠ 5 x≠ 0, x≠ 1 2 3 yes 4. g ( x ) = 3 x ( 3 x + 1 ) −( 1 + 9 x 2 ) ¿ 9 x 2 + 3 x 1 9 x 2 ¿ 3 x 1 ¿ ( 3 x 1 )( 2 x + 3 ) 2 x + 3 ¿ 6 x 2 2 x + 9 x 3 2 x + 3 ¿ 6 x 2 + 7 x 3 2 x + 3 ¿ f ( x ) g ( x ) = f ( x )
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As we can see, the expression g(x) is equal to the expression f(x). The function f(x) is not determined in point x= −1.5 while the domain for function g(x) is all real numbers. The only difference between the two functions is in the restrictions on the variable.
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yes 5. The function y =( x + 1 ) 2 8 is a quadratic function. The function y = x 3 is a square root function. The function y = 1 x + 4 is a reciprocal function. yes 6. a) y =( x + 1 ) 2 8 D ={ x R } R = { x R | y ≥ 8 } b) y = x 3 D = { x R | x≥ 3 } R = { y R | y ≥ 0 } c) y = 1 x + 4 D = { x R | x≠ 4 } R = { y R | y ≠ 0 } great
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7.
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  • Spring '18
  • Leigh
  • Graph of a function

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