PPT-Direct and Inverse Variation

Investigation 1 Ramp height and length vs time Direct vs Inverse y varies directly as x means y kx What does that graph look like y varies inversely as . Lesson 11-6. An equation in the form of ____________________ or . ____________ . is an inverse variation,. The constant of variation is _______, the _______________ of . . x. . and . y. for an ordered pair (x, y) that solves the inverse variation.. 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. Determine the asymptotes for:. Lesson . 3-8 . Direct, Inverse & Joint Variation. Objective: To recognize and use direct variation to solve problems. Definition:. . Y. varies directly as . x. means that . Section 5-2. Goals. Goal. To write and graph an equation of a direct variation.. Rubric. Level 1 – Know the goals.. Level 2 – Fully understand the goals.. Level 3 – Use the goals to solve simple problems.. 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]. . We know how to graph the inverse of a function, but now we will look into expressing a new inverse function. Like before, let’s keep in mind the “switching x and y” theory. f. -1. (x). The inverse of the function f(x), f. 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. Definition of Inverse Trig Functions. Graphs of inverse functions. Page 381. Ex. 1 Evaluating Inverse Trig Functions. a). arcsin. (-1/2). b). arcsin. (0.3). Properties of Inverse Functions. If -1≤x≤1 and –. When a problem states that variable X varies directly as variable Y, we know that the relationship implied is . . X = . kY. And that the first step in solving the problem is to find the value of the constant of proportionality k. . 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. . RATE. .. Direct Variation. Direct variation uses the following formula:. . Ossama. Inverse Matrix :. If . A. is a square matrix. , and if a . matrix . B. of the same size . can be found such that . AB = BA = I. , then . A. is said to be . invertible. and . B. is called an . Direct Variation. y varies directly as x if there is a nonzero constant, k, such that . y = . kx. *k is called the constant of variation. Plug in the two values you have and solve for the missing variable. Human variation: defined . Human variation refers to the fact that there are a range of possible values for each of the numerous physical characteristics of human beings.. People of the same species can have differing phenotypic traits that can be related to:.