Topic 1: Be able to combine functions and determine the resulting function. Topic 2: Be able to find the product of functions and determine the resulting.

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Presentation transcript:

Topic 1: Be able to combine functions and determine the resulting function. Topic 2: Be able to find the product of functions and determine the resulting function. Topic 3: Be able to perform multiple operations on functions. Topic 4: Determine if two given functions represent equivalent forms of the same function..

I. Multiplying Polynomial Functions Example 1: 3(2x + 6 ) (3)(2x) + (3)(6) 6x + 18 Example 2: -5(3x 2 – 6x + 4 ) (-5)(3x 2 ) + (-5)(– 6x) + (-5)(4) -15x x - 20 Concept: Constant x Linear = Linear Concept: Constant x Quadratic = Quadratic Example 3: 3(-4x 3 - 7x 2 + x + 2 ) (3)(-4x 3 ) + (3)(– 7x 2 ) + (3)(x) + (3)(2) -12x x 2 + 3x + 6 Concept: Constant x Cubic = Cubic

I. Multiplying Polynomial Functions Example 4: (3x + 4)(2x - 1) (3x)(2x - 1) + (4)(2x - 1) (3x)(2x ) + (3x)(-1)(4)(2x ) + (4)(-1)+ 6x 2 - 3x + 8x - 4 6x 2 + 5x - 4 3x4 2x 6x 2 8x -3x -4 6x 2 + 5x - 4 Concept: Linear x Linear= Quadratic Example 5: (-2x - 3)(6x + 7) (-2x)(6x + 7) + (-3)(6x + 7) (-2x)(6x ) + (-2x)(7)(-3)(6x ) + (-3)(7)+ -12x x - 18x x x x-3 6x 7 -12x 2 -18x -14x x 2 -32x - 21 Concept: Linear x Linear= Quadratic

I. Multiplying Polynomial Functions Example 6: (x - 3)(2x 2 – 7x + 5) (x)(2x 2 – 7x + 5) + (-3)(2x 2 - 7x + 5) (x)(2x 2 )+ (x)(– 7x) + (x)( 5)(-3)(2x 2 )+ (-3)(– 7x) + (-3)( 5)+ 2x 3 – 7x 2 + 5x-6x x x 3 – 13x x x 2 -7x5 x -3 2x 3 -7x 2 5x -6x 2 21x-15 2x 3 – 13x x - 15 Concept: Linear x Quadratic = Cubic

I. Multiplying Polynomial Functions Example 7: (5x 2 - 3)(3x 2 – 4x + 2) 5x 2 0x-3 3x 2 -4x 2 15x 4 0x 3 -9x 2 -20x 3 0x 2 12x 10x 2 0x-6 15x x 3 + x x - 6 Concept: Quadratic x Quadratic = Quartic Special Note: When setting up your table, be sure that you account for all terms of the polynomial.

I. Multiplying Polynomial Functions Example 8: (4x 2 – 3x + 2)(3x 2 + 6x - 5) 4x 2 -3x2 3x 2 6x -5 12x 4 -9x 3 6x 2 24x 3 -18x 2 12x -20x 2 15x-10 12x x x x - 10 Concept: Quadratic x Quadratic = Quartic