Equations Formula for Competitive Exams | Ias Banenge

Equations Formula:

Here in this page we will discuss all basic concept of Equations Formula. So, let’s get started.

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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 :

• a^x = c, a > 0
• If c > 0, a ≠ 1 : So one root x = log_a 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 :

loga_a 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 :

• α^A(x) > a^B(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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