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# Chapter0 - Chapter 0 Functions...

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Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 1 of 78 Chapter 0 Functions

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Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 2 of 78 Functions and Their Graphs Some Important Functions The Algebra of Functions Zeros of Functions – The Quadratic Formula and Factoring Exponents and Power Functions Functions and Graphs in Applications Chapter Outline
Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 3 of 78 § 0.1 Functions and Their Graphs

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Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 4 of 78 Rational and Irrational Numbers The Number Line Open and Closed Intervals Applications of Functions Domain of a Function Graphs of Functions The Vertical Line Test Graphing Calculators Graphs of Equations Section Outline
Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 5 of 78 Definition Example Rational Number : A number that may be written as a finite or infinite repeating decimal, in other words, a number that can be written in the form m / n such that m , n are integers Irrational Number : A number that has an infinite decimal representation whose digits form no repeating pattern 73205 . 1 3 = 285714 . 0 7 2 - = -

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Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 6 of 78 The Number Line A geometric representation of the real numbers is shown below. The Number Line -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 3 7 2 -
Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 7 of 78 Definition Example Open Interval : The set of numbers that lie between two given endpoints, not including the endpoints themselves Closed Interval : The set of numbers that lie between two given endpoints, including the endpoints themselves [-1, 4] -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 ( 29 , 4 4 x 4 1 - x

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Goldstein/Schneider/Lay/Asmar, CALCULUS AND ITS APPLICATIONS , 11e – Slide 8 of 78 Functions in Application EXAMPLE EXAMPLE SOLUTION SOLUTION ( Response to a Muscle ) When a solution of acetylcholine is introduced into the heart muscle of a frog, it diminishes the force with which the muscle contracts. The data from experiments of the biologist A. J. Clark are closely approximated by a function of the form where x is the concentration of acetylcholine (in appropriate units), b is a positive constant that depends on the particular frog, and R ( x ) is the response of the muscle to the acetylcholine, expressed as a percentage of the maximum possible effect of the drug. (a) Suppose that
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Chapter0 - Chapter 0 Functions...

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