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Unformatted text preview: c Kendra Kilmer January 20, 2009 Section 2.2 - Elementary Functions: Graphs and Transformations
Basic Elementary Functions Identity Function Square Function Cube Function Square Root Function Cube Root Function Absolute Value Function Example 1: Graph the following functions on the appropriate graph above. a) g(x) = x + 4 b) g(x) = x2 - 3 c) g(x) = (x - 1)3 d) g(x) = x + 3 e) g(x) = 4 3 x 1 f) g(x) = - |x| 2 6 c Kendra Kilmer January 20, 2009 Transformations 1. Vertical Transformation: g(x) = f (x) + k If k > 0, f (x) will move up k units. If k < 0, f (x) will move down |k| units. 2. Horizontal Transformation: g(x) = f (x - h) If h > 0, f (x) will move right h units. If h < 0, f (x) will move |h| units to the left. 3. Reflection, expansion, and contraction g(x) = a f (x) If |a| > 1, f (x) will stretch/expand vertically by a factor of a. If 0 < |a| < 1, f (x) will shrink/contract vertically by a factor of a. If a < 0, f (x) will be reflected about the x-axis. Example 2: If g(x) = -2 f (x + 1) - 3, describe how f (x) was transformed to get g(x)? 7 c Kendra Kilmer January 20, 2009 Definition: Functions whose definition involve more than one rule are called To graph, graph each rule over the appropriate portion of the domain. Example 3: Graph the following piecewise function: f (x) = x2 - 2 -2x + 3 if x < 0 if x 0 . Example 4: A taxi-cab company in a certain town charges all customers a base fee of $5 per ride. They then charge an additional 50 cents per mile for the first 10 miles traveled and $1/mile for each mile over 10 miles. Write a piecewise function, C(x), for the cost of a cab ride if x represents the number of miles traveled. Section 2.2 Homework Problems: 3,5,11,15,19,21,25,29,33,37,41,43,45,47,61,65,67 and supplemental problems 8 ...
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This note was uploaded on 03/27/2012 for the course MATH 142 taught by Professor Drost during the Fall '08 term at Texas A&M.
- Fall '08