PPT-Lesson 8-4: Direct, Joint, and Inverse Variation

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. . Relations. and . Functions. OBJ: . . . Find the . inverse. of a . relation. . . . . Draw the . graph. of a . function . and its . inverse. . . Determine whether the. 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.. 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 . 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 . 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.. 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. Inverse variation. Recall: variables . x . and . y. show direct variation if . for some nonzero constant . a. .. *Note: the general equation . for inverse variation can be rewritten as . ..  . Classifying direct/inverse variation. 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. 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:. 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). y = . kx. , where k ≠ 0. . The constant of variation for a direct variation . k. is the coefficient of . x.. Example of direct variation. : The time it takes to hear thunder varies directly with the distance from lightning. (As the distance from lightning increases, so does the time it takes you to hear the thunder!). SOL A.8. Slope and Constant Of Variation. Constant of Variation and Slope are the same thing!!!. Slope Formula. . m=.  . What is the slope of a line passing through (0,0) and (4,1).. m=. = . = . 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.