1. 1.4 BUILDING FUNCTIONS FROM FUNCTIONS By: Alaina Riedel & Lauren Evenson

2. “Building Blocks, Building Functions” f(x) = 2x -1 f(x) = |x +3| g(x) = 3 - x f(x) = 2 f(x) = 3x + 2 http://www.youtube.com/watch?v=9rsJF6lqxao Copy and Paste into Internet Explorer

3. 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, 4 - 5 = -1  The algebra of functions: fg, f-g, etc

4. Sum, Difference, Product, and Quotient

5. Composition of Functions

6. 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

7. Example - Relation

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

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

10. Materials Used  Pre-Calculus Book Pre-Calculus Book  http://facultypages.morris.umn.edu/~mcquarrb/te achingarchive/Precalculus/Lectures/BuildingFunction fromFunctions.pdf http://facultypages.morris.umn.edu/~mcquarrb/te achingarchive/Precalculus/Lectures/BuildingFunction fromFunctions.pdf  http://math.ucsd.edu/~wgarner/math4c/textbook/ chapter2/combfunctions.htm http://math.ucsd.edu/~wgarner/math4c/textbook/ chapter2/combfunctions.htm Jeopardy Game: https://jeopardylabs.com/https://jeopardylabs.com/