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1.7 FUNCTIONS

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CCSS Content Standards 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. Mathematical Practices 3 Construct viable arguments and critique the reasoning of others. Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

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You solved equation with elements from a replacement set. Determine whether a relation is a function. Evaluate functions.

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What is a Function? A function is a rule that establishes a relationship with an input and an output. Input ( x )Output ( y ) DOMAIN RANGE

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What is a Function? function – a relation where each input matches up with exactly one output Input ( x )Output ( y ) DOMAIN RANGE

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x (inputs) y (outputs) 1 20 31 53 86 f relation – a pairing of input (domain) and output (range) numbers

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x (inputs) y (outputs) 1 20 31 53 86 f relation – a pairing of input (domain) and output (range) numbers * A set of ordered pairs domain

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x (inputs) y (outputs) 1 20 31 53 86 f relation – a pairing of input (domain) and output (range) numbers domain range Domain = D {1, 2, 3, 5, 8} Range = R {-1, 0, 1, 3, 6} independent dependent

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xf (x) 3 03 13 33 63 63 33 Is f (x) a function? function – a relation where each input matches up with exactly one output If an input value is put in multiple times, you will get the same output every time. YES!

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xf (x) 13 013 1-3 43 65 65 31 Is f (x) a function? WHY? Check yourself! Does each input match up with exactly one output? If an input value is put in multiple times, do you get the same output every time? NO!

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How can I tell if it’s a function? REAL WORLD EXAMPLES

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People vs. Places

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Relation: Different Form {(1,-1),(2,0),(3,1),(5,6),(8,6)} Is this relation a function? Hint: Look at all of the input values first! {(1,-1),(2,0),(3,1),(5,6),(8,6)}

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Relation: Different Form {(1,-1),(2,0),(3,1),(5,6),(2,4)} Is this relation a function? {(1,-1),(2,0),(3,1),(5,6),(2,4)}

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x (inputs) y (outputs) -6-9 -5-7 3 24 67 3-7 Find: 1.domain 2.range 3.y if x = -1 4.x if y = 7 f

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For function f: y = 3 f (-1) = 3 function notation x (inputs) y (outputs) -6-9 -5-7 3 24 67 f “The value at x = -1 is 3.”

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xf (x) 13 013 1-3 43 65 65 31 Is f (x) a function? Vertical Line Test – as a vertical line passes it never touches more than one point on the graph NO! Graph it!

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Is g(x) a function? YES! Graph it! g(x) = -3x – 6 f (x) = mx + b linear function

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Is this a graph of a function? NOT A FUNCTION!

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Is this a graph of a function? FUNCTION!

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Evaluating Functions Remember f(x) is just function notation! A. If f(x) = 3x – 4, find f (4). f(4)=3(4) – 4Replace x with 4. =12 – 4Multiply. = 8Subtract. Answer: f (4) = 8

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B. If f(x) = 3x – 4, find f(–5).

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C. If h(t) = 1248 – 160t + 16t 2, find h(3).

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D. If f(x) = 4x+9 Find f(2) f(-3)+7 f(2y) EVALUATING CHALLENGE!!!

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The function h(t) = 180 – 16t 2 represents the height of a ball thrown from a cliff that is 180 feet above the ground. Find h(2z). APPLICATION CHALLENGE!!!

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Homework: 1.7 Practice Worksheet (ODDS) Algebra A/B

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