Chap_2_6_8 Slides.pdf - Math 124 Chapters 2.6/2.8...

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27 Slides Math 124 Chapters 2.6/2.8 Combinations of Functions; Composite Functions; Distance and Midpoint Formulas; Circles
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2 Find the domain of a function. Combine functions using the algebra of functions Form composite functions. Determine domains for composite functions. Write functions as compositions. Find the distance between two points. Find the midpoint of a line segment. Write the standard form of a circle’s equation. Give the center and radius of a circle whose equation is in standard form. Convert the general form of a circle’s equation to standard form. Objectives:
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3 Finding a Function’s Domain If a function f does not model data or verbal conditions, its domain is the largest set of real numbers for which the value of f ( x ) is a real number . Exclude from a function’s domain real numbers that cause division by zero and real numbers that result in a square (even) root of a negative number.
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4 Example: Finding the Domain of a Function Find the domain of the function Solution Because division by 0 is undefined, we must exclude from the domain the values of x that cause the denominator to equal zero. We exclude 7 and 7 from the domain of g . The domain of g is or 2 5 ( ) 49 x g x x 2 49 0 x 2 49 x 49 x   7 x   ( , 7) ( 7,7) (7, )   | 7,7 x x  
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