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Section 2.6 The Algebra of Functions

Section 2.6 The Algebra of Functions. Combining Two Functions Algebraically Sum: (f + g)(x) = f(x) + g(x) Difference: (f - g)(x) = f(x) - g(x) Product: (f · g)(x) = f(x) · g(x) Quotient: (f / g)(x) = f(x) / g(x) Domains & Graphs.

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Section 2.6 The Algebra of Functions

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  1. Section 2.6 The Algebra of Functions • Combining Two Functions Algebraically • Sum: (f + g)(x) = f(x) + g(x) • Difference: (f - g)(x) = f(x) - g(x) • Product: (f · g)(x) = f(x) · g(x) • Quotient: (f / g)(x) = f(x) / g(x) • Domains & Graphs 2.6

  2. Notation forSum, Difference, Product, Quotient of 2 Functions • When 2 functions are combined, they form a 3rd function, which may be able to be simplified “ f plus g of x “ 2.6

  3. Visualize the Two Functions (f + g)(x) = f(x) + g(x) (f + g)(x) = x + 4 + x2 + 1 (f + g)(x) = x2 + x + 5 check: (f + g)(2) = 22 + 2 + 5 = 11 2.6

  4. 2.6

  5. Domains and Graphs – Dietary Example from Univ. of CA Add these functions together: C(m) + P(m) + F(m) = (C + P + F)(m) 2.6

  6. Consider carefully:Domains Involving Quotients 2.6

  7. Domains of Combined Functions 2.6

  8. 2.6

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