PPT-3.2 Inverse Functions Functions

A function maps each element in the domain to exactly 1 element in the range Concept 1 Example 1 Domain and Range State the domain and range of the relation Then determine whether the relation is a function If it is a function determine if it is . 2x Leveraged ETF. . When index daily return rises 1%, ETF leveraged daily return rises 2%. 2X. -1x Inverse ETF. When index daily return drops 1%, ETF return rises 1%, hedging exposure to drop. -1X. 1X. CIDER seismology lecture IV. July 14, 2014. Mark Panning, University of Florida. Outline. The basics (forward and inverse, linear and non-linear). Classic discrete, linear approach. Resolution, error, and null spaces. A bit more practice in Section 4.7b. Analysis of the Inverse Sine Function. 1. –1. D:. R:. Continuous. Increasing. Symmetry: Origin (odd . func. .). Bounded. Abs. Max. of at . x. = 1. Abs. Min. of at . Goal: Use inverse variation and joint variation models.. Warm-up. Simplify:. Inverse Variation. 2 variables, x and y, vary inversely if:. k is called the constant of variation.. Example 1. Tell whether x and y show direct variation, inverse variation, or neither:. Section 5.6 Beginning on Page 276. What is the Inverse of a Function?. The inverse of a function is a generic equation to find the input of the original function when given the output [finding x when given y]. . Variation. What’s the Difference. Direct Variation. When we talk about a direct variation, we are talking about a relationship where as . x increases, . y increases. . or . decreases at a . CONSTANT. Functions. Composite Functions . (f. ◦. g)(x)=f(g(x)). Inverses and 1-to-1 Functions. Finding Formulas for Inverses. Graphing Functions and Their Inverses. Inverse Functions and Composition. 1980 . AB Free Response 3. Continuity and Differentiability of Inverses. If . f. . is continuous in its domain, then its inverse is continuous on its domain. . If . f. . is increasing on its domain, then its inverse is increasing on its domain . North Carolina Municipal Attorney’s Summer Conference . Asheville, August 6, 2010. 1. Inverse Condemnation – History and Nature of Action. “A taking without . formal . exercise of eminent domain” . The . inverse . of a relation is the set of ordered pairs obtained by . switching the input with the output. of each ordered pair in the original relation. (The domain of the original is the range of the inverse; and vice versa). SOL A8. by Robert Lotze, Moody Middle School. Direct Variation. The longer you shower, the more water you use.. You can describe this. Relationship using. . Direct Variation. The Direct Variation . . Engage NY: Lesson 5. Pink Packet pages 19-22. Write an expression to represent the temperature change.. In the morning, Harrison checked the temperature outside to find that it was -12°F. Later in the afternoon, the temperature rose 12°F. What was the afternoon temperature? . July 14, 2014. Mark Panning, University of Florida. Outline. The basics (forward and inverse, linear and non-linear). Classic discrete, linear approach. Resolution, error, and null spaces. Thinking more probabilistically. Page: . 108. Inverse:. The reversal of some process or operation.. For functions, the reversal involves the interchange of the domain. with the range.. Along with the reversal of the domain and range there is a reversal.