domain and range

domain and range : The mathematical concept of a function expresses the intuitive idea that one quantity (the argument of the function, also known as its input) completely determines another quantity (the value of the function or output). A function associates a unique value for each input of a specified type. Functions are a key notion of analysis, similarly to the way properties of numbers are fundamental to algebra and the study of shapes forms the basis of geometry. There are many ways to represent or visualize functions: a function may be described by a formula, by a plot or graph, by an algorithm that computes it, or by a description of its properties. Sometimes, a function is described through its relationship to other functions (see, for example, inverse function). In applied disciplines, functions are frequently specified by their tables of values. In pure mathematics, functions are defined using set theory, and there are theorems that show the existence of uncountably many..   More from Wikipedia

domain and range : The mathematical concept of a function expresses the intuitive idea that one quantity (the argument of the function, also known as its input) completely determines another quantity (the value of the function or output). A function associates a unique value for each input of a specified type. Functions..   More from Wikipedia

  Reading Domain and Range of a Relation From a Graph - Just a very basic idea of what the domain and range of a relation is, given a graph! For more free math videos, check out JustMathTutoring.com

  Finding the Domain and Range of a Piecewise Function - In this example I show how to find the domain and range of two previously graphed piecewise functions. For more free math videos visit JustMathTutoring.com

Question : f(x) = -5 + sqrt(9-x^2) I need to find the domain, range, and sketch a graph. Any help would be appreciated. For the graphing, if you could just explain that would help. Please be as thorough as possible so that I can do similar problems on my own. Thanks so much and 10 points to the best answer!

Answer : y=-5+ (9-x^2) 1) Domain 9-x^2 0 ==> 9 x^2 ==> |x| 3 ==> -3 x 3 Domain=[-3,3] 2) Range The easier way: x=0 ==> y=-5+ (9-0)=-5+3=-2 x= 3 ==>y=-5+ (9-9)=-5 Range=[-5,-2] The harder way: y+5= (9-x^2)>0..............(1) (y+5)^2=9-x^2 x^2+(y+5)^2=3^2.............(2) This is an equation of a circle with center at (0,-5) and radius r=3. From (1) and (2) ==> f(x)=-5+ (9-x^2) is the upper half of that circle ==> ymin=-5, ymax=-5+3=-2 Range=[-5,-2] 3) Graph: The upper half of the circle with center at (0,-5) and radius r=3. http://i299.photobucket.com/albums/mm286/rozeta53/halfcircle.jpg..   More from Yahoo Answers

Question : The question is , use transformation to sketch the graph of each of the following functions, starring with the graph of y=x^2. State the domain and range of each function. A) y=(x-5)^2 B) y=(x+7)^2 C) y=(x+2)^2 D) y=(x-3)^2 +4 Please don't worry about the graphing, i just want to know does transformation means to graph the opposite of it and please state the domain and ranges of them.THANKS

Answer : "The domain of all of them is the set of reals the range of the first three is y>=0, the fourth is y>=4 A) is shifted 5 units to the right B) is shifted 7 units to the left C) is shifter 2 units to the left D) is shifted 3 units to the right and up four units" Phoenixstarshine is spot on...   More from Yahoo Answers