Chapter 5 Section 5 MA1032 Data, Functions & Graphs Sidney - - PowerPoint PPT Presentation

Chapter 5 Section 5

MA1032 Data, Functions & Graphs Sidney Butler

Michigan Technological University

October 23, 2006

S Butler (Michigan Tech) Chapter 5 Section 5 October 23, 2006 1 / 8

Notation

x 1 2 3 4 5 6 f (x)

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3 7 12 f (x + 2) f (x − 2) f (x) + 2 f (x) − 2

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The Graph

f (x) = √x g(x) = f (x + 4) h(x) = f (x − 4)

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Any connection?

f (x) = x2 − 3 g(x) = x2 − 6x + 1

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1 2 3 4 5 6 7 8 9 10

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1 2 3 4 5 6 7 8 9 10

f(x)=x^2-3 g(x)=x^2-6x+1

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Graphic Distortion

f (x) = 2−x + 1 g(x) = 2−(x+1) + 1

1 2 3 4 5 1 2 3

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Group Exercise #36

For t ≥ 0, let H(t) = 68 + 93(0.91)t give the temperature of a cup of coffee in degrees Fahrenheit t minutes after it is brought to class.

1 Find formulas for H(t + 15) and H(t) + 15. 2 Graph H(t), H(t + 15), and H(t) + 15. 3 Describe in practical terms a situation modeled by the function

H(t + 15). What about H(t) + 15?

4 Which function H(t + 15) or H(t) + 15 approaches the same final

temperature as the function H(t)? What is that temperature?

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Some Extreme Examples

constant function linear function Challenge: Consider f (x) = mx + b. What horizontal shift gives the same result as a vertical shift of one unit up?

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Summary

Horizontal Shifts Vertical Shifts Formula from the Graph

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