1.4 BUILDING FUNCTIONS FROM FUNCTIONS By: Alaina Riedel & Lauren Evenson

“Building Blocks, Building Functions” f(x) = 2x -1 f(x) = |x +3| g(x) = 3 - x f(x) = 2 f(x) = 3x Copy and Paste into Internet Explorer

Combining Functions A way of creating new functions to combine two or more functions to create a new function.  The most obvious way we can do this is to perform basic algebraic operations on the two functions to create the new one  Add, subtract, multiply or divide functions.  The algebra of real numbers: 4 x 5 = 20, = -1  The algebra of functions: fg, f-g, etc

Sum, Difference, Product, and Quotient

Composition of Functions

Relations and Implicitly Defined Functions  Relation: A set of ordered pairs of real numbers - 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  Implicitly defined function: A function that is a subset of a relation defined by an equation in x and y

Example - Relation

Example - Implicitly The graph consists of two parallel lines, each the graph of one of the implicitly defined functions

 jeopardylabs.com /play/building-functions-from-functions2 Alaina & Lauren Mix Up

Materials Used  Pre-Calculus Book Pre-Calculus Book  achingarchive/Precalculus/Lectures/BuildingFunction fromFunctions.pdf achingarchive/Precalculus/Lectures/BuildingFunction fromFunctions.pdf  chapter2/combfunctions.htm chapter2/combfunctions.htm Jeopardy Game: