1.5 ­ Algebra of Functions (day 1)
Warm Up: Simplify completely.
1. (x2 ­ 3x)
(x2 ­ 9)
2. x + 3 3x ­ 2 x ­ 5
Given 2 functions f and g, new functions can be formed by adding, subtracting, multiplying, and dividing. The domain of the resulting function consists of the values of x common to the domains of both f and g.
Sum
Difference Product Quotient 1
Example 1: Given f(x) = 1 and g(x) = 2x
x ­ 3
a. f + g
find each function and state its domain.
b. f ­ g
Example 1(con't): Given f(x) = 1 and g(x) = 2x
x ­ 3
c. f * g
find each function and state its domain.
d. f / g
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Example 2 The total cost of airfare on a given route, excluding taxes and promotions, is comprised of the base cost C and the fuel surcharge S. Both C and S are functions of the mileage m; C(m) = 0.30m + 40 and S(m) = 0.02m. Determine a function for the total cost of a ticket in terms of the mileage, and find the airfare for flying 1573 miles.
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