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1-9 Introduction to Parent Functions Holt Algebra 2 Warm Up Lesson Presentation Lesson Quiz

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Identify parent functions from graphs and equations. Use parent functions to model real-world data and make estimates for unknown values. Objectives

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Similar to the way that numbers are classified into sets based on common characteristics, functions can be classified into families of functions . The parent function is the simplest function with the defining characteristics of the family. Functions in the same family are transformations of their parent function .

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Parent Functions

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To make graphs appear accurate on a graphing calculator, use the standard square window. Press ZOOM , choose 6:ZStandard , press again, and choose 5:ZSquare . Helpful Hint ZOOM ZOOM

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Identify the parent function for g from its function rule. Then graph g on your calculator and describe what transformation of the parent function it represents. Example 1A: Identifying Transformations of Parent Functions g ( x ) = x – 3

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Identify the parent function for g from its function rule. Then graph on your calculator and describe what transformation of the parent function it represents. Example 1B: Identifying Transformations of Parent Functions g ( x ) = x 2 + 5

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Check It Out! Example 1a g ( x ) = x 3 + 2 Identify the parent function for g from its function rule. Then graph on your calculator and describe what transformation of the parent function it represents.

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Check It Out! Example 1b g ( x ) = (– x ) 2 Identify the parent function for g from its function rule. Then graph on your calculator and describe what transformation of the parent function it represents.

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Remember that any parent function you use to approximate a set of data should never be considered exact. However, these function approximations are often useful for estimating unknown values. Consider the two data points (0, 0) and (0, 1) . If you plot them on a coordinate plane you might very well think that they are part of a linear function. In fact they belong to each of the parent functions below.

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Lesson Quiz: Part I Identify the parent function for g from its function rule. Then graph g on your calculator and describe what transformation of the parent function it represents. 1. g ( x ) = x + 7

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Lesson Quiz: Part II Identify the parent function for g from its function rule. Then graph g on your calculator and describe what transformation of the parent function it represents. 2. g ( x ) = x 2 – 7 quadratic; translation down 6 units

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Lesson Quiz: Part III 3. Stacy earns $7.50 per hour. Graph the relationship from hours to amount earned and identify which parent function best describes it. Then use the graph to estimate how many hours it would take Stacy to earn $60. linear: 8 hr

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