PPT-Inverse Functions Inverse Relations

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. . Relations. and . Functions. OBJ: . . . Find the . inverse. of a . relation. . . . . Draw the . graph. of a . function . and its . inverse. . . Determine whether the. Another natural way to define relations is to define both elements of the ordered pair (x, y), in terms of another variable . t. , called a . parameter. Parametric equations: . equations in the form. INVERSE FUNCTIONS. DO THIS NOW!. You have a function described by the equation: . f(x. ) = . x. + 4. The domain of the function is: {0, 2, 5, 10}. YOUR TASK: write the set of ordered pairs that would represent this function. Section 6.3 Beginning on page 310. Logarithms. For what value of x does . ? Logarithms can answer this question. Log is the inverse operation to undo unknown exponents. .  .  .  .  .  . *Read as log base b of y. Enea. Sacco. 2. Welcome to Calculus I!. Welcome to Calculus I. 3. Topics/Contents . Before Calculus. Functions. New functions from the old. Inverse Functions. Trigonometric Functions. Inverse Trigonometric Functions. Exponential and Logarithmic Functions. 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 5.6 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. 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 –. Int. Math 2. Vocabulary. Linear, non-linear, increasing, decreasing, rate of change, growth rate, domain, range, continuous, discontinuous, discrete, relation, function, inverse function, inverse . of a . 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 . Andrew Gardner, Slides 2-5, . Rafael Diaz, Slides . 9-11. Mosi. Davis. , Slides 6-8. What is the Inverse Function and how is it applied with currency?. The Inverse Function is a function used to return a value from x to y. For example: . 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.