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1.4 Building Functions from Functions

1.4 Building Functions from Functions. By: Alaina Riedel & Lauren Evenson . f(x) = 2x -1. “Building Blocks, Building Functions”. g(x) = . g(x) = 3 - x. g(x) = . f(x) = . f(x) = . f(x) = . g(x) = . g(x) = (x -1. f(x) = . g(x) = . f (x) = 3x + 2. g(x) = 9 - . g(x) = . f(x) = 2.

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1.4 Building Functions from Functions

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  1. 1.4 Building Functions from Functions By: Alaina Riedel & Lauren Evenson

  2. f(x) = 2x -1 “Building Blocks, Building Functions” g(x) = g(x) = 3 - x g(x) = f(x) = f(x) = f(x) = g(x) = g(x) = (x -1 f(x) = g(x) = f(x) = 3x + 2 g(x) = 9 - g(x) = f(x) = 2 f(x) = g(x) = f(x) = + 4 g(x) = f(x) = |x +3| g(x) = 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 • Determine which of the ordered pairs (2,-5), (1,3), and (2,1) are in the relation defined by + . Is this relation a function? (2,-5): (2(5) + (-5 = 5 (1,3): (1(3) + (3 = 12 = 5 (2,1): (2(1) + (1 = 5 So, (2,-5) and (2,1) are in the relation, but (1,3) is not. Since the equation relates two different y-values (-5 and 1) to the same x-value (2), the relation cannot be a function.

  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 • http://facultypages.morris.umn.edu/~mcquarrb/teachingarchive/Precalculus/Lectures/BuildingFunctionfromFunctions.pdf • http://math.ucsd.edu/~wgarner/math4c/textbook/chapter2/combfunctions.htm Jeopardy Game: https://jeopardylabs.com/

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