Function-DomainRange.pptVIP

Function - Domain Range Cubic, Circle, Hyperbola, etc By Mr Porter * X-axis Y-axis f(x)=(x-3)2(x+4) 0 0 h k (h,k) r r – r Definitions Function: A function is a set of ordered pair in which no two ordered pairs have the same x-coordinate. E.g. (3,5) (2,-2) (4,5) Domain - independent variable The domain of a function is the set of all x-coordinates or first element of the ordered pairs. [the values of x for which a vertical line will cut the curve.] Range - dependent variable The range of a function is the set of all y-coordinates or the second element of the ordered pairs. [the values of y for which a horizontal line will cut the curve] Note: Students need to be able to define the domain and range from the equation of a curve or function. It is encourage that student make sketches of each function, labeling each key feature. Cubic and Odd Power Functions. A general function can be written as f(x) = axn + bxn-1 + cxn-2 + …… + z where a ≠ 0 and n is a positive integer. If the power n is an ODD number, n = 3, 5, 7, ….. then f(x) is an odd powered function. We can generalise the domain and range as follows: Domain : All x in the real numbers, R. Range : All y in the real numbers, R. This is very true for the following functions: f(x) = 2x3 + 4 g(x) = 5 - x5 h(x) = x3 - x2 + 5x -7 X-axis Y-axis f(x)=-x(x-3)(x+4) X-axis Y-axis f(x)=(x-3)2(x+4) X-axis Y-axis f(x)=(x-3)(x+4)(x+1)(x-1) X-axis Y-axis f(x)=(x+3)2(x-4)3 X-axis Y-axis f(x)=2x3 Graphs of Odd Power Functions : n = 3 or 5 Every vertical line and horizontal line will cut the curve. Hence, Domain : all x in R Range : all y in R Circle There are to forms of the circle: a) Standard circle centred at the origin (0,0) radius r. x2 + y2 = r2 b) General circle, centred at (h,k) with radius r. (x - h)2 + (y - k)2 = r2 All circles are RELATIONS, but by restricting the RANGE, we convert them to functions. Standard Circle 1) x2 + y2 = 9 == x2 + y2 = 32 Circle centred (0,0), radius r = 3 units 3 3 -3 -3 X