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

3. Visualize the Two Functions
(f + g)(x) = f(x) + g(x)
(f + g)(x) = x x2 + 1
(f + g)(x) = x2 + x + 5
check:
(f + g)(2) = = 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)
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6. Consider carefully: Domains Involving Quotients
2.6

7. Domains of Combined Functions
2.6

8. 2.6