Equations Formula

Equations Formula:

What is linear equation ?
when equation between two variables that gives a straight line when plotted on a graph its called linear equation.

 

 

ax + b = 0,   a ≠ 0 ⇒    x = – b / a

 

 

Two Linear Equations :

a1 x + b1 y = c1                 a1 / a2 ≠ b1 / b2
a2 x + b2 y = c2


 

 

 

Exponential Equation :

  • ax = c,        a > 0
  • If c > 0, a ≠ 1 :  So one root x = loga c
    If c = 1, a = 1, So many roots,
    If c ≠ 1, a = 1, So no solution,
    If c ≤ = 0, no So no solution,

 

 

 

 

Logarithmic Equations :

logaa x = c (a > 0, a ≠ 1)
x = a c

 

 

Function Transformation Rule:

Horizontal Shifting :

g(x) = f(x – c)

 

 

 

 

Vertical Shifting :

g(x) = f(x) + c

 Stretching :

g(x) = c f(x), 0 < c < 1

h(x) = D f(x), D > 1

 

Reflection :

g(x) = f(-x)

h(x) = -f(x)

 

 

Exponential Inequation :

  • αA(x) > aB(x)
  • α > 0, A(x) > B(x)
  • 0< α < 1, A(x) < B(x)

 

 

 

Logarithmic Inequation :

loga α(x) = loga β(x)

  • a > 1:
  • β(x) > 0 , α(x) > β(x)

 

  • 0<a<1:
  • α(x) > 0, α(x) < β(x)

 

 

Other Functions Graph:

 

Square Root :

Parabolic:

 

 

Reciprocal :

 

 

Cubic :

Sec :

Cosec :


 

Absolute :


 

Constant :

 

 

 

 

 

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