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The function f (x) = x2 has a domain of all real numbers (x can be anything) and a range that is greater than or equal to zero Two ways in which the domain and range of a function can be written are interval notation and set notation Find the domain and range of the function f(x) = (x^2 9)/(x 3) asked in Sets, Relations and Functions by RamanKumar (499k points) sets;Algebra Find the Domain and Range f (x)=2/x f (x) = 2 x f ( x) = 2 x Set the denominator in 2 x 2 x equal to 0 0 to find where the expression is undefined x = 0 x = 0 The domain is all values of x x that make the expression defined Interval Notation

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 Substitute ah and a for x in the formula for f(x) and simplify to find (f(ah)f(a))/h = 2a 2 h >f(x) = x^22x3 Then (f(ah) f(a))/h =(((ah)^22(ah)3The quadratic function f (x) = a (x − h)2 k is in standard form (a) The graph of f is a parabola with vertex (x, y) = (b) If a > 0, the graph of f opens In this case f (h) = k is the value of f To find f (xh) substitute x = x h into the function f (x h) = (x h)2 − 2(x h) 5 now distribute the brackets f (x h) = x2 2hx h2 − 2x − 2h 5 which may be expressed as f (x h) = x2 2x(h −1) h2 − 2h 5 Answer link

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New users enjoy 60% OFF 167,742,297 stock photos online This is an extremely simple example, but it demonstrates level curves, and some following concepts very clearly So what are level curves showing?Given a function f(x,y), the set f(x,y) = c = const is called a contour curve or level curve of f For example, for f(x,y) = 4x2 3y2 the level curves f = c are ellipses if c > 0 Level curves allow to visualize functions of two variables f(x,y) Example For f(x,y) = x2 − y2 the set x2 − y2 = 0 is the union of the lines x = y and x = −y

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