Introduction to nonlinear equations

Introduction to nonlinear equations

Non-linear equations, as it says in its name, are any functions that are not linear, for example, quadratic, circle and exponential functions. In this lesson, we will learn how to graph nonlinear equations, and then determine whether they are a function or not. The easiest way to verify if an equation is a function, no matter if it is linear or non-linear, is by using the vertical line test.
Basic concepts: Solving linear equations by graphing, Identifying functions, Introduction to linear equations,
Related concepts: Graphing parabolas for given quadratic functions, Finding the quadratic functions for given parabolas, System of quadratic-quadratic equations, Graphing quadratic inequalities in two variables,

Lessons

Non-Linear
Equations: Basically any function that is not "linear equation", such as quadratic, circle, reciprocal, exponential, etc.
  • 1.
    Graph the following non-linear equations and determine if the relation is also a function.

    i) y=x2+2y = x^2 +2

    ii) x=12y2x = {1 \over 2} y^2

    iii) y=2xy = {2 \over x}

    iv) y=x−2y = \sqrt {x - 2}

    v) y=x3−2y = x^3 - 2

    vi) x2−y2=9x^2 - y^2 = 9
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4.
Linear Equations
4.1
Introduction to linear equations
4.2
Introduction to nonlinear equations
4.3
Special case of linear equations: Horizontal lines
4.4
Special case of linear equations: Vertical lines
4.5
Parallel line equation
4.6
Perpendicular line equation
4.7
Combination of both parallel and perpendicular line equations
4.8
Applications of linear equations
AU Maths Methods
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