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Integrated Algebra 2 Unit 1: Functions and Relations

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Soda Machine #1 Buttons Kinds of Sodas Dr. Pepper Coke Sprite Diet Coke Function? Yes, the soda machine gives you what you want! Domain/Image: BUTTONS – the input or independent variable D: { 1, 2, 3, 4} Range: SODA TYPES – the output or dependent variables R: {Dr. Pepper, Coke, Sprite, Diet Coke}

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Soda Machine #2 Buttons Kinds of Sodas Dr. Pepper Coke (high demand) Sprite Diet Coke Function? Yes, the soda machine gives you what you want! Domain/Image: BUTTONS - D: { 1, 2, 3, 4} Range: SODA TYPES – R: {Dr. Pepper, Coke, Sprite}

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Soda Machine #3 Buttons Kinds of Sodas Dr. Pepper Coke Sprite Diet Coke Function? MALFUNCTION – No, you could get two different sodas by pressing one button (dont know what to expect) Domain/Image: BUTTONS - D: { 1, 2, 3} Range: SODA TYPES – R: {Dr. Pepper, Coke, Sprite, Diet Coke} *Notice that the domain is smaller than the range – not a function!

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Definitions Relation: Any set of ordered pairs (any relationship between two variables) – Example: {(0,1), (1,4), (1,5), (6,2)} Function: A special type of relation where each input (independent variable) maps to only one unique output (dependent variable) – Example: {(0,1), (1,4), (2,5), (6,2)} – Does each x-value only appear once?

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Function Notation y = 3x + 1 reads y is a function of x where x is being multiplied by 3 and then 1 is added to the product f(x) = 3x + 1 reads a function of x where x is being multiplied by 3 and then 1 is added to the product So y = f(x)

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1. Given f(x) = {(0,3),(2,4),(-5,6),(4,1),(7,4)} Graph f(x) on the coordinate plane provided. Is this relation a function? How do you know? Yes, each input value has only one output (x- values are not repeated). State the domain of f(x). D: {0, 2, -5, 4, 7} OR {-5, 0, 2, 4, 7} State the range of f(x). R: {1, 3, 4, 6} Find f(4). Youre given an input of 4…what is the output? f(4) = 1 Find the x-value(s) such that f(x)=4. Youre given an output of 4..what is the input? x = 2 and x = 7

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2. Given g(x) = 1/x Find the range if the domain is {1, 2, 3, 4} *input the domain for x *R: {1/1, 1/2, 1/3, 1/4} or {1/4, 1/3, 1/2, 1} Will x = 0 ever be part of the domain in g(x)? Why? *No, you cant ever divide by zero!

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