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 ) -5 -3 0 3 7 12 f ( x + 2) f ( x − 2) f ( x ) + 2 f ( x ) − 2 S Butler (Michigan Tech) Chapter 5 Section 5 October 23, 2006 2 / 8
The Graph f ( x ) = √ x g ( x ) = f ( x + 4) h ( x ) = f ( x − 4) S Butler (Michigan Tech) Chapter 5 Section 5 October 23, 2006 3 / 8
Any connection? f ( x ) = x 2 − 3 g ( x ) = x 2 − 6 x + 1 10 f(x)=x^2-3 9 8 7 6 5 4 3 2 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 -7 g(x)=x^2-6x+1 -8 -9 -10 S Butler (Michigan Tech) Chapter 5 Section 5 October 23, 2006 4 / 8
Graphic Distortion f ( x ) = 2 − x + 1 g ( x ) = 2 − ( x +1) + 1 3 2 1 0 1 2 3 4 5 S Butler (Michigan Tech) Chapter 5 Section 5 October 23, 2006 5 / 8
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? S Butler (Michigan Tech) Chapter 5 Section 5 October 23, 2006 6 / 8
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? S Butler (Michigan Tech) Chapter 5 Section 5 October 23, 2006 7 / 8
Summary Horizontal Shifts Vertical Shifts Formula from the Graph S Butler (Michigan Tech) Chapter 5 Section 5 October 23, 2006 8 / 8
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