Section+1.4

=1.4 Building Fuctions from Fuctions!!!!!= //Things to know in this section:// -Combinging Functions Algebraically -Composition of Functions -Relations and Implicitly Defining Functions

The domain of the new function is the intersection of the domains f and g. (Page 117 in book)
 * Sum:** (f + g)(x) = f(x) + g(x)
 * Difference:** (f - g)(x) = f(x) - g(x)
 * Product:** (fg)(x) = f(x)g(x)
 * Quotient:** (f / g)(x) = f(x) / g(x), provided g(x) ≠ 0

examples: f(x) = x^2, g(x) = √x + 1 (just for clarification, √ is my sign for square root)

**ex 1:** (f + g)(x) = f(x) + g(x)
= x^2 + √x + 1 Domain: [-1, ∞)

**ex 2:** (f / g)(x) = f(x) / g(x)
= x^2 / (√x + 1)

x^2 (√x + 1)
Domain: [-1, ∞)

Let f and g be two functions such that the domain of f intersects the range of g. The __composition f of g__, denotes: (f of g)(x) = f(g(x)). example: f(x) = x^2 - 1, g(x) = √x g of f = g(f(x)) = g(x^2) = √x^2
 * __Composition of Functions:__** (Page 118 in book)

The general term for a set of ordered pairs (x,y) is a relation. If the relation happens to relate a single value of y to each value of x, then the relation is also a function and its graph will pass the vertical line test.
 * __Relations and Implicity__** ( Page 122-123 in book)

The circle with the equation x^2 + y^2 = 4, is not a function itself, but can be split into two equations that do define functions. x^2 + y^2 = 4 y^2 = 4 - x^2 y = + √4-x^2 or y = - √4-x^2 The graphs of these two functions are the upper and lower semicircles of the circle defined by x^2 + y^2 = 4. Because all ordered pairs in either of these functions satisfy the equation x^2 + y^2 = 4, we can say the relation given by the equation defines the two functions __implicitly__.

//__Homework!__// Monday: page 165; 25-37 odd Wednesday: page 124; 1-10 all