How to Draw a Function?

TopFunction is a Set of input and output, where each input is related to exactly one output. Suppose a set 'X' is input set also called as Domain and set 'Y' is output set also called co domain, and given function is f(x) = x2, so input value is x = (1, 2, 3), and output value is f (1) = 12 = 1, f (2) = 22 = 4, f(3) = 32 = 9 so y = (1, 4, 9).
Now we will see how to draw a function: There are some steps to draw a function.

Step 1: Suppose any equation px² + qx + r = 0 is given, so we have to check whether function is bottom up or down, we will check this by using 'p' if p > 0 then function is bottom up and if a < 0 then function is down.

Step 2: Find out vertex (-q/2p , f(-p/2q)).

Step 3: Find out x- intercept by using factor or Quadratic Formula.

Step 4: Find out y-intercept by plugging f(0).

Example: x² – 6x + 8?

Solution: Step 1: Here in this equation p = 1, q = -6, r = 8, here 1 > 0 , so this is bottom up.

Step 2: Vertex:- x = -q/2p = -(-6)/ 2*1 = 6/2 = > -q/2a = 3.
To find 'y' plug value of 'x' in the function f (1) = 9 – 18 + 8 = -1.
So vertex = (3 ,-1).

Step 3: x- intercept :- y, f(x) = 0
0 = x2 –6x + 8 => x2 – 4x - 2x +8 => x (x - 4) -2 (x - 4) => (x – 2)(x - 4) => x = 2, 4.
Y- intercept:- f(0) = 0 – 0 + 8 = 8, so y- intercept is 8, draw a graph using calculated values.
Graph: