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Integrated Algebra 2 Unit 1: Functions and Relations

Integrated Algebra 2 Unit 1: Functions and Relations. Soda Machine #1. Buttons Kinds of Sodas. 1. Dr. Pepper. 2. Coke. 3. Sprite. 4. Diet Coke. Function? Yes, the soda machine gives you what you want!

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Integrated Algebra 2 Unit 1: Functions and Relations

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  1. Integrated Algebra 2Unit 1: Functions and Relations

  2. Soda Machine #1 Buttons Kinds of Sodas 1 Dr. Pepper 2 Coke 3 Sprite 4 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}

  3. Soda Machine #2 Buttons Kinds of Sodas 1 Dr. Pepper 2 Coke (high demand) 3 Sprite 4 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}

  4. Soda Machine #3 Buttons Kinds of Sodas 1 Dr. Pepper 2 Coke 3 Sprite 4 Diet Coke Function? MALFUNCTION – No, you could get two different sodas by pressing one button (don’t 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!

  5. 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?

  6. 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” Soy= f(x)

  7. 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). You’re given an input of 4…what is the output? f(4) = 1 • Find the x-value(s) such that f(x)=4. You’re given an output of 4..what is the input? x = 2 and x = 7

  8. 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 ing(x)? Why? *No, you can’t ever divide by zero!

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