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Combining Functions

Combining Functions. MCC9-12.F.BF.1b Combine standard function types using arithmetic operations. . Adding Linear Functions . f(x) + g(x) If f(x)= 3x - 4 and g(x) = -2x + 6, find f(x) + g(x). (3x – 4) + (-2x + 6) OR 3x – 4 + -2x +6 1x + 2 So, f(x) + g(x) = 1x + 2.

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Combining Functions

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  1. Combining Functions MCC9-12.F.BF.1b Combine standard function types using arithmetic operations.

  2. Adding Linear Functions • f(x) + g(x) • If f(x)= 3x - 4 and g(x) = -2x + 6, find f(x) + g(x). • (3x – 4) + (-2x + 6) OR • 3x – 4 + -2x +6 1x + 2 • So, f(x) + g(x) = 1x + 2

  3. Adding Linear Functions • If f(x) = 7x + 3 and g(x) = 6x – 4, find f(x) + g(x).

  4. Subtracting Linear Functions • f(x) - g(x) • If f(x) = 4x -29 and g(x)= 2x – 18, find f(x) – g(x). • (4x – 29) – (2x -18) change – to + the opposite. • (4x – 29) + (-2x +18) • 4x – 29 + -2x + 18 2x - 11 • So, f(x) – g(x) = 2x – 11

  5. Subtracting Linear Functions • If f(x) = -3x + 15 and g(x) = -4x -17, find f(x) – g(x).

  6. Multiplying Linear Functions • f(x) · g(x) • If f(x) = 3x and g(x) = 2x -17, find f(x)·g(x). • (3x)(2x-17) = 3x(2x) – 3x(17) = 6x2 – 51 • So, f(x) · g(x) = 6x2 – 51

  7. Multiplying Linear Functions • If f(x) = x - 13 and g(x) = -5x, find f(x)·g(x).

  8. Dividing Linear Functions • f(x) / g(x) • If f(x) = 6x and g(x) = 2x, find f(x)/g(x). • 6x/2x = 3 • So, f(x) / g(x) = 3

  9. Dividing Linear Functions • If f(x) = x + 5 and g(x) = 2x, find f(x)/g(x).

  10. Adding exponential functions • f(x) + g(x) • If f(x) = 2x and g(x) = 2x, find f(x) + g(x). • 2x + 2x = 2(2x)

  11. Adding exponential functions • If f(x) = 2(4x) and g(x) = 4x, find f(x) + g(x)

  12. Subtracting exponential functions • f(x) – g(x) • If f(x) = 5(8x) and g(x) = 2(8x), find f(x) – g(x). • 5(8x) – 2(8x) = 3(8x) • So f(x) – g(x) = 3(8x)

  13. Subtracting exponential functions • If f(x) = 4(6x) and g(x) = 7(6x), find f(x) – g(x).

  14. Multiplying exponential functions • If f(x) = 52x and g(x) = 5x, then find f(x)·g(x). • 52x · 5x = 52x + x = 53x • When multiplying exponential functions, bases must be the same. You add the exponents. • So f(x) · g(x) = 53x

  15. Multiplying exponential functions • If f(x) = 8(9)x and g(x) = 1/2(9)-2x, find f(x) · g(x).

  16. Dividing Exponential Functions • f(x)/g(x) • If f(x) = 8(26x) and g(x) = 4(23x), find f(x)/g(x). • 8(26x) = 2(23x) 4(23x)

  17. Dividing Exponential Functions • If f(x) = 8(94x) and g(x) = 2(9-3x), find f(x)/g(x).

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