Graphic Function

Look at two pictures below!

Drawing a Graphic Function Do you still remember about Coordinate System? Cartesian Coordinate System has two axis, which is X-Axis and Y-Axis 1) Horizontal axis (X-axis or Abscissa) is an axis that states the value of x 2) Vertical axis (Y-axis or ordinate) is the axis that states the value of y = f (x) 3) The point (x 1, y 1 ) is a point with abscissa x 1 and ordinate y 1 = f (x 1 )

How to draw Graphic Function 1.Given a function f: x  x + 2 from set A = {0, 1, 2, 3, 4} to a set of whole number. Make a mapping table f as follows: x01234 f(x)23456 (x, f(x))(0,2)(1,3)(2,4)(3,5)(4,6)

2. Draw the graph of the function based on previous mapping x01234 f(x)23456 (x, f(x))(0,2)(1,3)(2,4)(3,5)(4,6) As you can see, the graph only consists of points (no line). It’s all because we use a set of whole number Then what kind of number that we can use to draw a line?

Example Make a mapping table for f: x  2x – 1 from a set {x|-2 ≤ x ≥ 2, x Є R} to a set of real numbers. Then, draw its graph. Answer: 1.To do easier work, choose some x with integer. Then make a chart mapping x-2012 f(x)2(-2)-1=52(-1)-1=-32(0)-1=-12(1)-1=12(2)-1=3 (x, f(x))(-2,-5)(-1,-3)(0,-1)(1,1)(2,3)

2. 2. Draw the graph of the function based on previous mapping x-2012 f(x) (x, f(x))(-2,-5)(-1,-3)(0,-1)(1,1)(2,3) As you can see, the graph is a line while we use a set of real number

Linear Function Linear function is a function f on the set of real numbers R is defined by f(x) = ax + b with a, b real numbers, and a ≠ 0

Linear function f (x) = ax + b with a <0 has a graph of a straight line with the smaller value of the function for values ​​ of x greater Example: Graph of f(x) = 3x + 2

Linear function f (x) = ax + b with a> 0 have a graph is a straight line with the greater value of the function for values ​​ of x greater Example: Graph of f(x) = -x + 4

Quadratic Function Quadratic function is a function f on the set of real numbers R is defined by f(x) = ax 2 + bx + c with a, b, c real numbers and a ≠ 0

The function f (x) with a> 0 has a graph in the form of an upward opened parabola Example: f(x) = x 2 + 2x - 3

The function f (x) with a <0 has a graph in the form of a down opened parabola Example: f(x) = x - 2x 2

Given a graph, as you can see x = 0 while f(0) = 3, by using function formula f(x)= ax + b F(0)= a(0) + b 3= b See others points x = -1,5 while f(-1,5) = 0 f(x)= ax + b F(-1,5)= a(-1,5) + 3 0= -1,5a + 3 a = 2 So function formula of the graph is f(x) = 2x + 3