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# Alg II 2-1 Relations and Functions

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### Alg II 2-1 Relations and Functions

1. 1. Algebra II Chapter 2 Functions, Equations, and Graphs
2. 2.  Essential Understanding: a pairing of items from tow sets is special if each item from one set pairs exactly with one item from the second set. Essential Understanding: some quantities are in a relationship where the ratio of corresponding values is constant Objectives:  Students will be able to graph relations  Students will be able to identify functions  Students will be able to write and interpret direct variation equations
3. 3.  Functions – (Review) F-IF.1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). F-IF.2. Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
4. 4.  Algebra A-CED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Functions F-IF.1. Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). F-BF.1. Write a function that describes a relationship between two quantities.★ Determine an explicit expression, a recursive process, or steps for calculation from a context.
5. 5.  Set of pairs of input and output values Represented in four different ways  Ordered Pair Mapping Diagram  Table of Values Graph
6. 6.  The monthly average water temperature of the Gulf of Mexico in Key west, Florida varies during the year. In January, the average temperature is 69 degrees, in February, 70 degrees, in March, 75 degrees, and in April, 78 degrees. How can you represent this relation?
7. 7.  What is domain?  Input values of a relation/function (x-coordinates) What is range?  Output values of a relation/function (y- coordinates) What is the domain and range of the relation? {(-3, 14), (0, 7), (2, 0), (9, -18), (23, -99)}
8. 8.  A relation in which each element of the domain corresponds with exactly one element of the range.
9. 9.  On a graph you can use the vertical line test to determine if the relation is a function.
10. 10.  Function Rule: an equation that represents an output value in terms on an input value Function Notation: uses f(x) = equation Independent Variable: x, represents the input of a function Dependent Variable: f(x) or y, represents the output of a function For f(x) = -4(x) + 1, what is the output for the given inputs: -2, 0, and 5?
11. 11.  A pizza costs \$14; the flat delivery fee is \$1.50. What function rule models the total cost of the number of pizzas delivered. Evaluate for 5 pizzas.
12. 12.  Pg. 64 #1 –26 all, 32, 3428 problems